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Bayesian Analysis with Python

You're reading from   Bayesian Analysis with Python A practical guide to probabilistic modeling

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Product type Paperback
Published in Jan 2024
Publisher Packt
ISBN-13 9781805127161
Length 394 pages
Edition 3rd Edition
Languages
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Author (1):
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Osvaldo Martin Osvaldo Martin
Author Profile Icon Osvaldo Martin
Osvaldo Martin
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Table of Contents (15) Chapters Close

Preface
1. Chapter 1 Thinking Probabilistically FREE CHAPTER 2. Chapter 2 Programming Probabilistically 3. Chapter 3 Hierarchical Models 4. Chapter 4 Modeling with Lines 5. Chapter 5 Comparing Models 6. Chapter 6 Modeling with Bambi 7. Chapter 7 Mixture Models 8. Chapter 8 Gaussian Processes 9. Chapter 9 Bayesian Additive Regression Trees 10. Chapter 10 Inference Engines 11. Chapter 11 Where to Go Next 12. Bibliography
13. Other Books You May Enjoy
14. Index

2.5 Posterior predictive checks

One of the nice elements of the Bayesian toolkit is that once we have a posterior p(θ|Y ), it is possible to use it to generate predictions p(Ỹ). Mathematically, this can be done by computing:

 ∫ p(˜Y | Y ) = p(˜Y | θ) p(θ | Y )dθ

This distribution is known as the posterior predictive distribution. It is predictive because it is used to make predictions, and posterior because it is computed using the posterior distribution. So we can think of this as the distribution of future data given the model, and observed data.

Using PyMC is easy to get posterior predictive samples; we don’t need to compute any integral. We just need to call the sample_posterior_predictive function and pass the InferenceData object as the first argument. We also need to pass the model object, and we can use the extend_inferencedata argument to add the posterior predictive samples to the InferenceData object. The code is:

Code 2.14

pm.sample_posterior_predictive(idata_g, model=model_g, ...
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