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

4.11 Exercises

  1. Using the howell dataset (available at https://github.com/aloctavodia/BAP3), create a linear model of the weight (x) against the height (y). Exclude subjects that are younger than 18. Explain the results.

  2. For four subjects, we get the weights (45.73, 65.8, 54.2, 32.59), but not their heights. Using the model from the previous exercise, predict the height for each subject, together with their 50% and 94% HDIs. Tip: Use pm.MutableData.

  3. Repeat exercise 1, this time including those below 18 years old. Explain the results.

  4. It is known for many species that weight does not scale with height, but with the logarithm of the weight. Use this information to fit the howell data (including subjects from all ages).

  5. See the accompanying code model_t2 (and the data associated with it). Experiment with priors for ν, like the non-shifted Exponential and Gamma priors (they are commented on in the code). Plot the prior distribution to ensure that you understand them. An easy...