<\/p>\n\n\n\n
<\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Thank you.<\/p>\n\n\n\n
<\/p>\n\n\n\n
<\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n
Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Probabilistic-Programming-and-Bayesian-Methods-for-Hackers<\/a> is a fantastic book to appreciate the Bayesian framework and techniques in greater depth from programmers' point-of-view.<\/p>\n\n\n\n Thank you.<\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n","post_title":"Bayesian Inference - MCMC","post_excerpt":"","post_status":"publish","comment_status":"open","ping_status":"open","post_password":"","post_name":"bayesian-inference-mcmc","to_ping":"","pinged":"","post_modified":"2020-04-12 18:48:40","post_modified_gmt":"2020-04-12 13:18:40","post_content_filtered":"","post_parent":0,"guid":"http:\/\/pm-powerconsulting.com\/?p=14090","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}],"next":false,"prev":false,"total_page":1},"paged":1,"column_class":"jeg_col_3o3","class":"epic_block_11"};
Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n We do not want an overconfident prediction framework that just relies on the data and provides a point estimate about the future. Besides, we can't afford to wait for a large dataset to perform the prediction in leisure. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Our intention is not to exactly predict the count of how many people will be infected in the next few days. We all pray for it to be zero. I'm not going to do that in this post.<\/p>\n\n\n\n We do not want an overconfident prediction framework that just relies on the data and provides a point estimate about the future. Besides, we can't afford to wait for a large dataset to perform the prediction in leisure. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n Our intention is not to exactly predict the count of how many people will be infected in the next few days. We all pray for it to be zero. I'm not going to do that in this post.<\/p>\n\n\n\n We do not want an overconfident prediction framework that just relies on the data and provides a point estimate about the future. Besides, we can't afford to wait for a large dataset to perform the prediction in leisure. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n <\/p>\n\n\n\n Our intention is not to exactly predict the count of how many people will be infected in the next few days. We all pray for it to be zero. I'm not going to do that in this post.<\/p>\n\n\n\n We do not want an overconfident prediction framework that just relies on the data and provides a point estimate about the future. Besides, we can't afford to wait for a large dataset to perform the prediction in leisure. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n <\/p>\n\n\n\n Our intention is not to exactly predict the count of how many people will be infected in the next few days. We all pray for it to be zero. I'm not going to do that in this post.<\/p>\n\n\n\n We do not want an overconfident prediction framework that just relies on the data and provides a point estimate about the future. Besides, we can't afford to wait for a large dataset to perform the prediction in leisure. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n A bar graph of the observation is here for your reference.<\/p>\n\n\n\n <\/p>\n\n\n\n Our intention is not to exactly predict the count of how many people will be infected in the next few days. We all pray for it to be zero. I'm not going to do that in this post.<\/p>\n\n\n\n We do not want an overconfident prediction framework that just relies on the data and provides a point estimate about the future. Besides, we can't afford to wait for a large dataset to perform the prediction in leisure. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\n You can access the Jupyter Notebook I've used for the analysis from here https:\/\/github.com\/krsmanian1972\/bayes\/blob\/master\/COVID-19-India.ipynb<\/a>. <\/p>\n\n\n\n We collected the count of new cases, of COVID-19 diseases, per day from Apr 1 to Apr 11. The source https:\/\/en.wikipedia.org\/wiki\/2020_coronavirus_pandemic_in_India<\/a><\/p>\n\n\n\n A bar graph of the observation is here for your reference.<\/p>\n\n\n\n <\/p>\n\n\n\n Our intention is not to exactly predict the count of how many people will be infected in the next few days. We all pray for it to be zero. I'm not going to do that in this post.<\/p>\n\n\n\n We do not want an overconfident prediction framework that just relies on the data and provides a point estimate about the future. Besides, we can't afford to wait for a large dataset to perform the prediction in leisure. <\/p>\n\n\n\n The I believe that the number of cases will not grow exponentially for various reasons. <\/p>\n\n\n\n The framework allows us to incorporate these beliefs as Priors.<\/p>\n\n\n\n At the same time I don\u2019t want to be super optimistic and be a daydreamer. I always align my hypothesis in the Likelihood of new evidence made available to me. The new evidence may be either an increase or a decrease in the number of new cases reported on a day. <\/p>\n\n\n\n Of course, If you have a different belief, nothing stops you from incorporating your prior beliefs until our beliefs are washed away by the new evidences.<\/p>\n\n\n\n So the priors and the likelihoods are the key ingredients of the Bayesian framework. Our endeavor here is, use the prior and the likelihood to calculate the posterior probability - The probability of the hypothesis given the observed evidence.<\/p>\n\n\n\n Poisson distribution is appropriate to model the number of times an event occurs in an interval of time or space<\/em>. The daily count of patients tested positive for the disease forms a discrete probability distribution and can be perfectly modeled with the Poisson distribution.<\/p>\n\n\n\n The probability of observing k patients in an interval can be calculated using this famous probability mass function equation of Poisson distribution. <\/p>\n\n\n\n Where \u019b is the rate parameter that drives the Poisson distribution and is unfortunately hidden from us, because of multiple possible mappings between the rate parameter and the set of data. <\/p>\n\n\n\n An interesting property of the Poisson distribution is its expected value equals this rate parameter - \u019b. Hence the distribution of latent \u019b is the representation of the risk ahead.<\/p>\n\n\n\n The rest of the exercise is to infer the distribution of the rate parameters, \u019bs, given the observed patient data. <\/p>\n\n\n\n More precisely, exploring the posterior probabilities of this rate parameter given the observed data is the ultimate aim of our exercise. <\/p>\n\n\n\n We will use PyMC3, which is a Python library for performing Bayesian analysis and to obtain the posterior distribution of \u019bs.<\/p>\n\n\n\n Let us start by importing the required python library components and create an array to hold the daily count of infected people as sourced from COVID-19 Wiki.<\/p>\n\n\n\n As stated earlier, our aim is to obtain the distribution of \u019bs. Let us work backward which is a common pattern in probabilistic programming to explore the distribution.<\/p>\n\n\n\n Remember that the number of patients on a day is Poisson distributed. In a Poisson distribution the expected value on a particular day is the posterior value of \u019b. <\/p>\n\n\n\n Now we have a distribution instead of a point-estimate. Hence we can expect any count from 540 to 580 in a day but should admit the uncertainty. <\/p>\n\n\n\n Though the priors for the \u019b have been randomly sampled from an exponential distribution, we could infer that it is not likely for the number of cases to grow exponentially, as of now, given the data we received.<\/p>\n\n\n\n I acknowledge that our inference will be very unstable with such a small set of data. I\u2019m fine with that. <\/p>\n\n\n\n I leave it to the readers to perform a change-point analysis after 5 days from today. I hope to see a mixed Poisson distribution in the observed data with reduced lambda patterns.<\/p>\n\n\n\n The PyMC3 Library uses a family of algorithm called Markov Chain Monte Carlo methods- MCMC to generate the posterior distribution. In our next post, we will code one such algorithm using RUST lang<\/a><\/p>\n\n\n\nArtifacts<\/h3>\n\n\n\n
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Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
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Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
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Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
Fitting the Model<\/h3>\n\n\n\n
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Next<\/h3>\n\n\n\n
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Motive<\/h3>\n\n\n\n
Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
Fitting the Model<\/h3>\n\n\n\n
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Next<\/h3>\n\n\n\n
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Motive<\/h3>\n\n\n\n
Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
Fitting the Model<\/h3>\n\n\n\n
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Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
Fitting the Model<\/h3>\n\n\n\n
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Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
Fitting the Model<\/h3>\n\n\n\n
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Modeling <\/h3>\n\n\n\n
Result<\/h3>\n\n\n\n
<\/figure>\n\n\n\n
Inference<\/h3>\n\n\n\n
Next<\/h3>\n\n\n\n
Artifacts<\/h3>\n\n\n\n
<\/figure>\n\n\n\n
Motive<\/h3>\n\n\n\n
Bayesian inference <\/a>framework<\/a><\/code> is our choice because it supports us to incorporate our prior, optimistic, beliefs and at the same time helps us to align our inferences based on new evidences. The most significant feature of Bayesian inference is its ability to expose the degree of uncertainties in our predictions. The philosophy is Courage and fail-fast.<\/p>\n\n\n\n
Fitting the Model<\/h3>\n\n\n\n
<\/figure><\/div>\n\n\n\n
Modeling <\/h3>\n\n\n\n
Result<\/h3>\n\n\n\n
<\/figure>\n\n\n\n
Inference<\/h3>\n\n\n\n
Next<\/h3>\n\n\n\n