\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"};

Page 1 of 2 1 2
\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"};

Page 1 of 2 1 2
\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"};

\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"};

\n

Artifacts<\/h3>\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"};

\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

Artifacts<\/h3>\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"};

\n

Next<\/h3>\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

Artifacts<\/h3>\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"};

\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\n

Inference<\/h3>\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\n
\"\"<\/figure>\n\n\n\n

Inference<\/h3>\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\n

Result<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Inference<\/h3>\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\n
\"\"
Code to Define the model and drawing the samples<\/figcaption><\/figure>\n\n\n\n

Result<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Inference<\/h3>\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

\n[gist https:\/\/gist.github.com\/krsmanian1972\/4f5f86406302e4e480c02866dbaca9d3 \/]\n\n\n\n
\"\"
Code to Define the model and drawing the samples<\/figcaption><\/figure>\n\n\n\n

Result<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Inference<\/h3>\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

Next<\/h3>\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

Artifacts<\/h3>\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"};

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