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 3
Hierarchical Models

Hierarchical models are one honking great idea – let’s do more of those! - The zen of Bayesian modeling

In Chapter 2, we saw a tips example where we had multiple groups in our data, one for each of Thursday, Friday, Saturday, and Sunday. We decided to model each group separately. That’s sometimes fine, but we should be aware of our assumptions. By modeling each group independently, we are assuming the groups are unrelated. In other words, we are assuming that knowing the tip for one day does not give us any information about the tip for another day. That could be too strong an assumption. Would it be possible to build a model that allows us to share information between groups? That’s not only possible, but is also the main topic of this chapter. Lucky you!

In this chapter, we will cover the following topics:

  • Hierarchical models

  • Partial pooling

  • Shrinkage