Book Image

Bayesian Analysis with Python - Third Edition

By : Osvaldo Martin
Book Image

Bayesian Analysis with Python - Third Edition

By: Osvaldo Martin

Overview of this book

The third edition of Bayesian Analysis with Python serves as an introduction to the main concepts of applied Bayesian modeling using PyMC, a state-of-the-art probabilistic programming library, and other libraries that support and facilitate modeling like ArviZ, for exploratory analysis of Bayesian models; Bambi, for flexible and easy hierarchical linear modeling; PreliZ, for prior elicitation; PyMC-BART, for flexible non-parametric regression; and Kulprit, for variable selection. In this updated edition, a brief and conceptual introduction to probability theory enhances your learning journey by introducing new topics like Bayesian additive regression trees (BART), featuring updated examples. Refined explanations, informed by feedback and experience from previous editions, underscore the book's emphasis on Bayesian statistics. You will explore various models, including hierarchical models, generalized linear models for regression and classification, mixture models, Gaussian processes, and BART, using synthetic and real datasets. By the end of this book, you will possess a functional understanding of probabilistic modeling, enabling you to design and implement Bayesian models for your data science challenges. You'll be well-prepared to delve into more advanced material or specialized statistical modeling if the need arises.
Table of Contents (15 chapters)
Preface
12
Bibliography
13
Other Books You May Enjoy
14
Index

10.7 Convergence

Theoretically, MCMC methods are guaranteed to converge once we take infinite samples. In practice, we need to check that we have reasonable finite samples. Usually, we say the sampler has converged once we have collected evidence showing that samples are stable in some sense. A simple test to do is to run the same MCMC simulation multiple times and check whether we get the same result every time. This is the reason why PyMC runs more by default than on chain. For modern computers, this is virtually free as we have multiple cores. Also, they do not create any waste, as we can combine samples from different chains to compute summaries, plots, etc.

There are many ways to check that different chains are practically equivalent, both visually and with formal tests. We are not going to get too technical here; we are just going to show a few examples and hope they are enough for you to develop an intuition for interpreting diagnostics.

10.7.1 Trace plot

One way to check...