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Bayesian Analysis with Python

By : Osvaldo Martin

3.1 (16)

Buy this Book

Bayesian Analysis with Python

3.1 (16)

By: Osvaldo Martin

Buy this Book

Overview of this book

The second edition of Bayesian Analysis with Python is an introduction to the main concepts of applied Bayesian inference and its practical implementation in Python using PyMC3, a state-of-the-art probabilistic programming library, and ArviZ, a new library for exploratory analysis of Bayesian models. The main concepts of Bayesian statistics are covered using a practical and computational approach. Synthetic and real data sets are used to introduce several types of models, such as generalized linear models for regression and classification, mixture models, hierarchical models, and Gaussian processes, among others. By the end of the book, you will have a working knowledge of probabilistic modeling and you will be able to design and implement Bayesian models for your own data science problems. After reading the book you will be better prepared to delve into more advanced material or specialized statistical modeling if you need to.

Preface

Who this book is for

What this book covers

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Free Chapter

Thinking Probabilistically

Statistics, models, and this book's approach

Probability theory

Single-parameter inference

Communicating a Bayesian analysis

Posterior predictive checks

Summary

Exercises

Programming Probabilistically

Probabilistic programming

PyMC3 primer

Summarizing the posterior

Gaussians all the way down

Groups comparison

Hierarchical models

Summary

Exercises

Modeling with Linear Regression

Simple linear regression

Robust linear regression

Hierarchical linear regression

Polynomial regression

Multiple linear regression

Variable variance

Summary

Exercises

Generalizing Linear Models

Generalized linear models

Logistic regression

Multiple logistic regression

Poisson regression

Robust logistic regression

The GLM module

Summary

Exercises

Model Comparison

Posterior predictive checks

Occam's razor – simplicity and accuracy

Information criteria

Bayes factors

Regularizing priors

WAIC in depth

Summary

Exercises

Mixture Models

Mixture models

Finite mixture models

Non-finite mixture model

Continuous mixtures

Summary

Exercises

Gaussian Processes

Linear models and non-linear data

Modeling functions

Gaussian process regression

Regression with spatial autocorrelation

Gaussian process classification

Cox processes

Summary

Exercises

Inference Engines

Inference engines

Non-Markovian methods

Markovian methods

Diagnosing the samples

Summary

Exercises

Where To Go Next?

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Inference Engines

"The first principle is that you must not fool yourself—and you are the easiest person to fool."

- Richard Feynman

So far, we have focused on model building, interpretation of results and criticism of models. We have relied on the magic of the pm.sample function to compute the posterior distributions for us. Now we will focus on learning some of the details of the inference engines behind this function. The whole purpose of probabilistic programming tools, such as PyMC3, is that the user should not care about how sampling is carried out, but understanding how we get samples from the posterior is important for a full understanding of the inference process, and could also help us to get an idea of when and how these methods fail and what to do about it. If you are not interested in understanding how the methods for approximating the posterior...