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

8.7 Gaussian process classification

In Chapter 4, we saw how a linear model can be used to classify data. We used a Bernoulli likelihood with a logistic inverse link function. Then, we applied a boundary decision rule. In this section, we are going to do the same, but this time using a GP instead of a linear model. As we did with model_lrs from Chapter 4, we are going to use the iris dataset with two classes, setosa and versicolor, and one predictor variable, the sepal length.

For this model, we cannot use the pm.gp.Marginal class, because that class is restricted to Gaussian likelihoods as it takes advantage of the mathematical tractability of the combination of a GP prior with a Gaussian likelihood. Instead, we need to use the more general class pm.gp.Latent.

Code 8.7

with pm.Model() as model_iris: 
    ℓ = pm.InverseGamma('ℓ', *get_ig_params(x_1)) 
    cov = pm.gp.cov.ExpQuad(1, ℓ) 
&...