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.

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Table of Contents (11 chapters)
Preface
Preface
Who this book is for
What this book covers
To get the most out of this book
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1
Thinking Probabilistically
Thinking Probabilistically
Statistics, models, and this book's approach
Probability theory
Single-parameter inference
Communicating a Bayesian analysis
Posterior predictive checks
Summary
Exercises
2
Programming Probabilistically
Programming Probabilistically
Probabilistic programming
PyMC3 primer
Summarizing the posterior
Gaussians all the way down
Groups comparison
Hierarchical models
Summary
Exercises
3
Modeling with Linear Regression
Modeling with Linear Regression
Simple linear regression
Robust linear regression
Hierarchical linear regression
Polynomial regression
Multiple linear regression
Variable variance
Summary
Exercises
4
Generalizing Linear Models
Generalizing Linear Models
Generalized linear models
Logistic regression
Multiple logistic regression
Poisson regression
Robust logistic regression
The GLM module
Summary
Exercises
5
Model Comparison
Model Comparison
Posterior predictive checks
Occam's razor – simplicity and accuracy
Information criteria
Bayes factors
Regularizing priors
WAIC in depth
Summary
Exercises
6
Mixture Models
Mixture Models
Mixture models
Finite mixture models
Non-finite mixture model
Continuous mixtures
Summary
Exercises
7
Gaussian Processes
Gaussian Processes
Linear models and non-linear data
Modeling functions
Gaussian process regression
Regression with spatial autocorrelation
Gaussian process classification
Cox processes
Summary
Exercises
8
Inference Engines
Inference Engines
Inference engines
Non-Markovian methods
Markovian methods
Diagnosing the samples
Summary
Exercises
9
Where To Go Next?
Where To Go Next?
10
Other Books You May Enjoy
Other Books You May Enjoy
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Exercises

  1. For the example in the Covariance functions and kernels section make sure you understand the relationship between the input data and the generated covariance matrix. Try using other input such as data = np.random.normal(size=4)
  2. Rerun the code generating Figure 7.3 and increase the number of samples obtained from the GP-prior to around 200. In the original figure the number of samples is 2. Which is the range of the generated values?
  3. For the generated plot in the previous exercise. Compute the standard deviation for the values of at each point. Do this in the following form:
    • Visually, just observing the plots
    • Directly from the values generated from stats.multivariate_normal.rvs
    • By inspecting the covariance matrix (if you have doubts go back to exercise 1)

Did the values you get from these 3 methods agree?

  1. Re-run the model model_reg and get new plots but...
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