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

7.10 Exercises

  1. Generate synthetic data from a mixture of 3 Gaussians. Check the accompanying Jupyter notebook for this chapter for an example of how to do this. Fit a finite Gaussian mixture model with 2, 3, or 4 components.

  2. Use LOO to compare the results from exercise 1.

  3. Read and run through the following examples about mixture models from the PyMC documentation:

    • Marginalized Gaussian mixture model: https://www.pymc.io/projects/examples/en/latest/mixture_models/marginalized_gaussian_mixture_model.html

    • Dependent density regression: https://www.pymc.io/projects/examples/en/latest/mixture_models/dependent_density_regression.html

  4. Refit fish_data using a NegativeBinomial and a Hurdle NegativeBinomial model. Use rootograms to compare these two models with the Zero-Inflated Poisson model shown in this chapter.

  5. Repeat exercise 1 using a Dirichlet process.

  6. Assuming for a moment that you do not know the correct species/labels for the iris dataset, use a mixture model to cluster the...