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

Chapter 5
Comparing Models

A map is not the territory it represents, but, if correct, it has a similar structure to the territory. – Alfred Korzybski

Models should be designed as approximations to help us understand a particular problem or a class of related problems. Models are not designed to be verbatim copies of the real world. Thus, all models are wrong in the same sense that maps are not the territory. But not all models are equally wrong; some models will be better than others at describing a given problem.

In the previous chapters, we focused our attention on the inference problem, that is, how to learn the values of parameters from data. In this chapter, we are going to focus on a complementary problem: how to compare two or more models for the same data. As we will learn, this is both a central problem in data analysis and a tricky one. In this chapter, we are going to keep examples super simple, so we can focus on the technical aspects of model comparison. In...