Book Image

Bayesian Analysis with Python - Second Edition

By : Osvaldo Martin
4.5 (2)
Book Image

Bayesian Analysis with Python - Second Edition

4.5 (2)
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.

Related Content you might be interested in

Current Title:

Small book image
Bayesian Analysis with Python - Second Edition
Osvaldo Martin
Dec, 2018 | 356 pages
Small book image
R Statistics Cookbook
Francisco Juretig
Mar, 2019 | 448 pages
Small book image
Training Systems Using Python Statistical Modeling.
Curtis Miller
May, 2019 | 290 pages
Small book image
Enhancing Deep Learning with Bayesian Inference
Marian Schneider | Matt Benatan | Jochem Gietema
Jun, 2023 | 386 pages
Table of Contents (11 chapters)
Preface
Preface
Who this book is for
What this book covers
To get the most out of this book
Get in touch
Free Chapter
1
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
2
Programming Probabilistically
Programming Probabilistically
Probabilistic programming
PyMC3 primer
Summarizing the posterior
Gaussians all the way down
Groups comparison
Hierarchical models
Summary
Exercises
3
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
4
Generalizing Linear Models
Generalizing Linear Models
Generalized linear models
Logistic regression
Multiple logistic regression
Poisson regression
Robust logistic regression
The GLM module
Summary
Exercises
5
Model Comparison
Model Comparison
Posterior predictive checks
Occam's razor – simplicity and accuracy
Information criteria
Bayes factors
Regularizing priors
WAIC in depth
Summary
Exercises
6
Mixture Models
Mixture Models
Mixture models
Finite mixture models
Non-finite mixture model
Continuous mixtures
Summary
Exercises
7
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
8
Inference Engines
Inference Engines
Inference engines
Non-Markovian methods
Markovian methods
Diagnosing the samples
Summary
Exercises
9
Where To Go Next?
Where To Go Next?
10
Other Books You May Enjoy
Other Books You May Enjoy
Leave a review - let other readers know what you think

The GLM module

As we discussed at the beginning of this chapter, linear models are very useful statistical tools. Extensions such as the ones we saw in this chapter make them even more general tools. For that reason, PyMC3 includes a module to simplify the creation of linear models: the Generalized Liner Model (GLM) module. For example, a simple linear regression will be as follows:

with pm.Model() as model: 
    glm.glm('y ~ x', data) 
    trace = sample(2000)

The second line of the preceding code takes care of adding priors for the intercept and for the slope. By default, the intercept is assigned a flat prior, and the slopes an prior. Note that the maximum a posteriori (MAP) of the default model will be essentially equivalent to the one obtained using the ordinary least squared method. These is totally fine as a default linear regression; you can change it using...

Previous Section
End of Section 7
Next Section