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

5.8 Regularizing priors

Using informative and weakly informative priors is a way of introducing bias in a model and, if done properly, this can be really good because bias prevents overfitting and thus contributes to models being able to make predictions that generalize well. This idea of adding a bias element to reduce generalization errors without affecting the ability of the model to adequately model a problem is known as regularization. This regularization often takes the form of a term penalizing certain values for the parameters in a model, like too-big coefficients in a regression model. Restricting parameter values is a way of reducing the data a model can represent, thus reducing the chances that a model will capture noise instead of the signal.

This regularization idea is so powerful and useful that it has been discovered several times, including outside the Bayesian framework. For regression models, and outside Bayesian statistics, two popular regularization methods are ridge...