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.
Table of Contents (11 chapters)
9
Where To Go Next?

Gaussian process regression

Let's assume we can model a value as a function of plus some noise:

Here

This is similar to the assumption that we made in Chapter 3, Modeling with Linear Regression, for linear regression models. The main difference is that now we will put a prior distribution over . Gaussian processes can work as such a prior, thus we can write:

Here, represents a Gaussian process distribution, with being the mean function and the kernel, or covariance, function. Here, we have used the word function to indicate that, mathematically, the mean and covariance are infinite objects, even when, in practice, we always work with finite objects.

If the prior distribution is a GP and the likelihood is a normal distribution, then the posterior is also a GP and we can compute it analytically:


Here:

is the observed data point and represents the test points...