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Bayesian Analysis with Python

By : Osvaldo Martin

3.2 (17)

Bayesian Analysis with Python

3.2 (17)

By: Osvaldo Martin

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

Preface

Who this book is for

What this book covers

To get the most out of this book

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Free Chapter

Thinking Probabilistically

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

Programming Probabilistically

Probabilistic programming

PyMC3 primer

Summarizing the posterior

Gaussians all the way down

Groups comparison

Hierarchical models

Summary

Exercises

Modeling with Linear Regression

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

Generalizing Linear Models

Generalized linear models

Logistic regression

Multiple logistic regression

Poisson regression

Robust logistic regression

The GLM module

Summary

Exercises

Model Comparison

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

Mixture models

Finite mixture models

Non-finite mixture model

Continuous mixtures

Summary

Exercises

Gaussian Processes

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

Inference engines

Non-Markovian methods

Markovian methods

Diagnosing the samples

Summary

Exercises

Where To Go Next?

Where To Go Next?

Other Books You May Enjoy

Other Books You May Enjoy

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Multiple logistic regression

In a similar fashion to multiple linear regression, multiple logistic regression is about using more than one independent variable. Let's try combining the sepal length and the sepal width. Remember we need to pre-process the data a little bit:

df = iris.query("species == ('setosa', 'versicolor')") 
y_1 = pd.Categorical(df['species']).codes 
x_n = ['sepal_length', 'sepal_width'] 
x_1 = df[x_n].values

The boundary decision

Feel free to skip this section and jump to the model implementation (next section) if you are not too interested in how we can derive the boundary decision.

From the model, we have the following equation:

And from...

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