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

10.9 Monte Carlo standard error

Even if we have a very low and a very high value of ESS. The samples from MCMC are still finite, and thus we are introducing an error in the estimation of the posterior parameters. Fortunately, we can estimate the error, and it is called the Monte Carlo Standard Error (MCSE). The estimation of the MCSE takes into account that the samples are not truly independent of each other. The precision we want in our results is limited by this value. If the MCSE for a parameter is 0.2, it does not make sense to report a parameter as 2.54. Instead, if we repeat the simulation (with a different random seed), we should expect that for 68% of the results, we obtain values in the range 2.54 ± 0.2. Similarly, for 95% of them, we should get values in the range 2.54 ± 0.4. Here, I am assuming the MCSE distributes normally and then using the fact that 68% of the value of a Gaussian is within one standard deviation and 95% is within two standard...