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

5.2 The balance between simplicity and accuracy

When choosing between alternative explanations, there is a principle known as Occam’s razor. In very general terms, this principle establishes that given two or more equivalent explanations for the same phenomenon, the simplest is the preferred explanation. A common criterion of simplicity is the number of parameters in a model.

There are many justifications for this heuristic. We are not going to discuss any of them; we are just going to accept them as a reasonable guide.

Another factor that we generally have to take into account when comparing models is their accuracy, that is, how good a model is at fitting the data. According to this criterion, if we have two (or more) models and one of them explains the data better than the other, then that is the preferred model.

Intuitively, it seems that when comparing models, we tend to prefer those that best fit the data and those that are simple. But what should we do if these two principles...