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

6.9 Variable selection

Variable selection refers to the process of identifying the most relevant variables in a model from a larger set of potential predictors. We perform variable selection under the assumption that only a subset of variables have a considerable impact on the outcome of interest, while others contribute little or no additional value.

Arguably the ”most Bayesian thing to do” when building a model is to include all the variables that we may think of in a single model and then use the posterior from that model to make predictions or gain an understanding of the relationships of the variables. This is the ”most Bayesian” approach because we are using as much data as possible and incorporating in the posterior the uncertainty about the importance of the variables. However, being more Bayesian than Bayes is not always the best idea. We already saw in Chapter 5 that Bayes factors can be problematic, even when they are a direct consequence of Bayes...