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

3.6 Summary

In this chapter, we have presented one of the most important concepts to learn from this book: hierarchical models. We can build hierarchical models every time we can identify subgroups in our data. In such cases, instead of treating the subgroups as separate entities or ignoring the subgroups and treating them as a single group, we can build a model to partially pool information among groups. The main effect of this partial pooling is that the estimates of each subgroup will be biased by the estimates of the rest of the subgroups. This effect is known as shrinkage and, in general, is a very useful trick that helps to improve inferences by making them more conservative (as each subgroup informs the others by pulling estimates toward it) and more informative. We get estimates at the subgroup level and the group level.

Paraphrasing the Zen of Python, we can certainly say hierarchical models are one honking great idea, let’s do more of those! In the following chapters...