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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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Regression with spatial autocorrelation

The following example is taken from the book, Statistical Rethinking, by Richard McElreath. The author kindly allowed me to reuse his example here. I strongly recommend reading his book, as you will find many good examples like this and very good explanations. The only caveat is that the book examples are in R/Stan, but don't worry and keep sampling; you will find the Python/PyMC3 version of those examples in https://github.com/pymc-devs/resources.

Well, going back to the example, we have 10 different island-societies; for each one of them, we have the number of tools they use. Some theories predict that larger populations develop and sustain more tools than smaller populations. Another important factor is the contact rates among populations.

As we have number of tools as dependent variable, we can use a Poisson regression with the...