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

5.3 Measures of predictive accuracy

”Everything should be made as simple as possible, but not simpler” is a quote often attributed to Einstein. As in a healthy diet, when modeling, we have to maintain a balance. Ideally, we would like to have a model that neither underfits nor overfits the data. We want to somehow balance simplicity and goodness of fit.

In the previous example, it is relatively easy to see that the model of order 0 is too simple, while the model of order 5 is too complex. In order to get a general approach that will allow us to rank models, we need to formalize our intuition about this balance of simplicity and accuracy.

Let’s look at a couple of terms that will be useful to us:

  • Within-sample accuracy: The accuracy is measured with the same data used to fit the model.

  • Out-of-sample accuracy: The accuracy measured with data not used to fit the model.

The within-sample accuracy will, on average, be greater than the out-of-sample accuracy. That is...