Book Image

Bayesian Analysis with Python - Third Edition

By : Osvaldo Martin
Book Image

Bayesian Analysis with Python - Third Edition

By: Osvaldo Martin

Overview of this book

The third edition of Bayesian Analysis with Python serves as an introduction to the main concepts of applied Bayesian modeling using PyMC, a state-of-the-art probabilistic programming library, and other libraries that support and facilitate modeling like ArviZ, for exploratory analysis of Bayesian models; Bambi, for flexible and easy hierarchical linear modeling; PreliZ, for prior elicitation; PyMC-BART, for flexible non-parametric regression; and Kulprit, for variable selection. In this updated edition, a brief and conceptual introduction to probability theory enhances your learning journey by introducing new topics like Bayesian additive regression trees (BART), featuring updated examples. Refined explanations, informed by feedback and experience from previous editions, underscore the book's emphasis on Bayesian statistics. You will explore various models, including hierarchical models, generalized linear models for regression and classification, mixture models, Gaussian processes, and BART, using synthetic and real datasets. By the end of this book, you will possess a functional understanding of probabilistic modeling, enabling you to design and implement Bayesian models for your data science challenges. You'll be well-prepared to delve into more advanced material or specialized statistical modeling if the need arises.
Table of Contents (15 chapters)
Preface
12
Bibliography
13
Other Books You May Enjoy
14
Index

10.4 Markovian methods

There is a family of related methods, collectively known as the Markov chain Monte Carlo or MCMC methods. These are stochastic methods that allow us to get samples from the true posterior distribution as long as we can compute the likelihood and the prior point-wise. You may remember that this is the same condition we needed for the grid method, but contrary to them, MCMC methods can efficiently sample from higher-probability regions in very high dimensions.

MCMC methods visit each region of the parameter space following their relative probabilities. If the probability of region A is twice that of region B, we will obtain twice as many samples from A as we will from B. Hence, even if we are not capable of computing the whole posterior analytically, we could use MCMC methods to take samples from it. In theory, MCMC will give us samples from the correct distribution – the catch is that this theoretical guarantee only holds asymptotically, that is, for an infinite...