Bayesian networks with examples in R

Table of Contents
Preface to the Second Edition
Preface to the First Edition

1. The Discrete Case: Multinomial Bayesian Networks
Introductory Example: Train Use Survey
Graphical Representation
Probabilistic Representation
Estimating the Parameters: Conditional Probability Tables
Learning the DAG Structure: Tests and Scores
Conditional Independence Tests
Network Scores
Using Discrete Bayesian Networks
Using the DAG Structure
Using the Conditional Probability Tables
Exact Inference
Approximate Inference
Plotting Discrete Bayesian Networks
Plotting DAGs
Plotting Conditional Probability Distributions
Further Reading

2. The Continuous Case: Gaussian Bayesian Networks
Introductory Example: Crop Analysis
Graphical Representation
Probabilistic Representation
Estimating the Parameters: Correlation Coefficients
Learning the DAG Structure: Tests and Scores
Conditional Independence Tests
Network Scores
Using Gaussian Bayesian Networks
Exact Inference
Approximate Inference
Plotting Gaussian Bayesian Networks
Plotting DAGs
Plotting Conditional Probability Distributions
More Properties
Further Reading

3. The Mixed Case: Conditional Gaussian Bayesian Networks
Introductory Example: Healthcare Costs
Graphical and Probabilistic Representation
Estimating the Parameters: Mixtures of Regressions
Learning the DAG Structure: Tests and Scores
Using Conditional Gaussian Bayesian Networks
Further Reading

4. Time Series: Dynamic Bayesian Networks
Introductory Example: Domotics
Graphical Representation
Probabilistic Representation
Learning a Dynamic Bayesian Network
Using Dynamic Bayesian Networks
Plotting Dynamic Bayesian Networks
Further Reading

5. More Complex Cases: General Bayesian Networks
Introductory Example: A&E Waiting Times
Graphical and Probabilistic Representation
Building the Model in Stan
Generating Data
Exploring the Variables
Estimating the Parameters in Stan
Further Reading

6. Theory and Algorithms for Bayesian Networks
Conditional Independence and Graphical Separation
Bayesian Networks
Markov Blankets
Moral Graphs
Bayesian Network Learning
Structure Learning
Constraint-based Algorithms
Score-based Algorithms
Hybrid Algorithms
Parameter Learning
Bayesian Network Inference
Probabilistic Reasoning and Evidence
Algorithms for Belief Updating
Exact Inference Algorithms
Approximate Inference Algorithms
Causal Bayesian Networks
Evaluating a Bayesian Network
Further Reading

7. Software for Bayesian Networks
An Overview of R Packages
The deal Package
The catnet Package
The pcalg Package
The abn Package
Stan and BUGS Software Packages
Stan: a Feature Overview
Inference Based on MCMC Sampling
Other Software Packages
BayesiaLab
Hugin
GeNIe

8. Real-World Applications of Bayesian Networks
Learning Protein-Signalling Networks
A Gaussian Bayesian Network
Discretising Gene Expressions
Model Averaging
Choosing the Significance Threshold
Handling Interventional Data
Querying the Network
Predicting the Body Composition
Aim of the Study
Designing the Predictive Approach
Assessing the Quality of a Predictor
The Saturated BN
Convenient BNs
Looking for Candidate BNs
Further Reading

A Graph Theory
A Graphs, Nodes and Arcs
A The Structure of a Graph
A Further Reading

B Probability Distributions
B General Features
B Marginal and Conditional Distributions
B Discrete Distributions
B Binomial Distribution
B Multinomial Distribution
B Other Common Distributions
B Bernoulli Distribution
B Poisson Distribution
B Continuous Distributions
B Normal Distribution
B Multivariate Normal Distribution
B Other Common Distributions
B Chi-square Distribution
B Student’s t Distribution
B Beta Distribution
B Dirichlet Distribution
B Conjugate Distributions
B Further Reading

C A Note about Bayesian Networks
C Bayesian Networks and Bayesian Statistics

Bayesian Networks: With Examples in R, Second Edition introduces Bayesian networks using a hands-on approach. Simple yet meaningful examples illustrate each step of the modelling process and discuss side by side the underlying theory and its application using R code. The examples start from the simplest notions and gradually increase in complexity. In particular, this new edition contains significant new material on topics from modern machine-learning practice: dynamic networks, networks with heterogeneous variables, and model validation.

The first three chapters explain the whole process of Bayesian network modelling, from structure learning to parameter learning to inference. These chapters cover discrete, Gaussian, and conditional Gaussian Bayesian networks. The following two chapters delve into dynamic networks (to model temporal data) and into networks including arbitrary random variables (using Stan). The book then gives a concise but rigorous treatment of the fundamentals of Bayesian networks and offers an introduction to causal Bayesian networks. It also presents an overview of R packages and other software implementing Bayesian networks. The final chapter evaluates two real-world examples: a landmark causal protein-signalling network published in Science and a probabilistic graphical model for predicting the composition of different body parts.

Covering theoretical and practical aspects of Bayesian networks, this book provides you with an introductory overview of the field. It gives you a clear, practical understanding of the key points behind this modelling approach and, at the same time, it makes you familiar with the most relevant packages used to implement real-world analyses in R. The examples covered in the book span several application fields, data-driven models and expert systems, probabilistic and causal perspectives, thus giving you a starting point to work in a variety of scenarios.