book

Bayesian Networks, 2nd Edition

Name: Bayesian Networks, 2nd Edition
ISBN: 9781000410396

by Marco Scutari, Jean-Baptiste Denis

July 2021

Intermediate to advanced

274 pages

6h 50m

English

Chapman and Hall/CRC

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Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface to the Second Edition
Preface to the First Edition
1 The Discrete Case: Multinomial Bayesian Networks
1.1 Introductory Example: Train-Use Survey1.2 Graphical Representation1.3 Probabilistic Representation1.4 Estimating the Parameters: Conditional Probability Tables1.5 Learning the DAG Structure: Tests and Scores1.5.1 Conditional Independence Tests1.5.2 Network Scores1.6 Using Discrete Bayesian Networks1.6.1 Using the DAG Structure1.6.2 Using the Conditional Probability Tables1.6.2.1 Exact Inference1.6.2.2 Approximate Inference1.7 Plotting Discrete Bayesian Networks1.7.1 Plotting DAGs1.7.2 Plotting Conditional Probability Distributions1.8 Further Reading

2 The Continuous Case: Gaussian Bayesian Networks
2.1 Introductory Example: Crop Analysis2.2 Graphical Representation2.3 Probabilistic Representation2.4 Estimating the Parameters: Correlation Coefficients2.5 Learning the DAG Structure: Tests and Scores2.5.1 Conditional Independence Tests2.5.2 Network Scores2.6 Using Gaussian Bayesian Networks2.6.1 Exact Inference2.6.2 Approximate Inference2.7 Plotting Gaussian Bayesian Networks2.7.1 Plotting DAGs2.7.2 Plotting Conditional Probability Distributions2.8 More Properties2.9 Further Reading
3 The Mixed Case: Conditional Gaussian Bayesian Networks
3.1 Introductory Example: Healthcare Costs3.2 Graphical and Probabilistic Representation3.3 Estimating the Parameters: Mixtures of Regressions3.4 Learning the DAG Structure: Tests and Scores3.5 Using Conditional Gaussian Bayesian Networks3.6 Further Reading
4 Time Series: Dynamic Bayesian Networks
4.1 Introductory Example: Domotics4.2 Graphical Representation4.3 Probabilistic Representation4.4 Learning a Dynamic Bayesian Network4.5 Using Dynamic Bayesian Networks4.6 Plotting Dynamic Bayesian Networks4.7 Further Reading
5 More Complex Cases: General Bayesian Networks
5.1 Introductory Example: A&E Waiting Times5.2 Graphical and Probabilistic Representation5.3 Building the Model in Stan5.3.1 Generating Data5.3.2 Exploring the Variables5.4 Estimating the Parameters in Stan5.5 Further Reading
6 Theory and Algorithms for Bayesian Networks
6.1 Conditional Independence and Graphical Separation6.2 Bayesian Networks6.3 Markov Blankets6.4 Moral Graphs6.5 Bayesian Network Learning6.5.1 Structure Learning6.5.1.1 Constraint-Based Algorithms6.5.1.2 Score-Based Algorithms6.5.1.3 Hybrid Algorithms6.5.2 Parameter Learning6.6 Bayesian Network Inference6.6.1 Probabilistic Reasoning and Evidence6.6.2 Algorithms for Belief Updating6.6.2.1 Exact Inference Algorithms6.6.2.2 Approximate Inference Algorithms6.7 Causal Bayesian Networks6.8 Evaluating a Bayesian Network6.9 Further Reading
7 Software for Bayesian Networks
7.1 An Overview of R Packages7.1.1 The deal Package7.1.2 The catnet Package7.1.3 The pcalg Package7.1.4 The abn Package7.2 Stan and BUGS Software Packages7.2.1 Stan: A Feature Overview7.2.2 Inference Based on MCMC Sampling7.3 Other Software Packages7.3.1 BayesiaLab7.3.2 Hugin7.3.3 GeNIe
8 Real-World Applications of Bayesian Networks
8.1 Learning Protein-Signalling Networks8.1.1 A Gaussian Bayesian Network8.1.2 Discretising Gene Expressions8.1.3 Model Averaging8.1.4 Choosing the Significance Threshold8.1.5 Handling Interventional Data8.1.6 Querying the Network8.2 Predicting the Body Composition8.2.1 Aim of the Study8.2.2 Designing the Predictive Approach8.2.2.1 Assessing the Quality of a Predictor8.2.2.2 The Saturated BN8.2.2.3 Convenient BNs8.2.3 Looking for Candidate BNs8.3 Further Reading
A Graph Theory
A.1 Graphs, Nodes and ArcsA.2 The Structure of a GraphA.3 Further Reading
B Probability Distributions
B.1 General FeaturesB.2 Marginal and Conditional DistributionsB.3 Discrete DistributionsB.3.1 Binomial DistributionB.3.2 Multinomial DistributionB.3.3 Other Common DistributionsB.3.3.1 Bernoulli DistributionB.3.3.2 Poisson DistributionB.4 Continuous DistributionsB.4.1 Normal DistributionB.4.2 Multivariate Normal DistributionB.4.3 Other Common DistributionsB.4.3.1 Chi-Square DistributionB.4.3.2 Student's t DistributionB.4.3.3 Beta DistributionB.4.3.4 Dirichlet DistributionB.5 Conjugate DistributionsB.6 Further Reading
C A Note about Bayesian Networks
C.1 Bayesian Networks and Bayesian Statistics
Glossary
Solutions
Bibliography
Index

Content preview from Bayesian Networks, 2nd Edition

6

Theory and Algorithms for Bayesian Networks

In this chapter we will provide the theoretical foundations underpinning the classes of BNs we explored in the previous chapters. In particular, we will introduce the formal definition of a BN and its fundamental properties. We will then show how these properties provide a rigorous foundation for BN learning and inference.

6.1 Conditional Independence and Graphical Separation

BNs are a class of graphical models, which allow an intuitive representation of the probabilistic structure of multivariate data using graphs. We introduced them in Chapter 1 as the combination of:

A set of random variables $X = {X_{1}, X_{2}, \dots, X_{p}}$ describing the quantities of interest. The multivariate probability distribution ...

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Bayesian Networks, 2nd Edition

by Marco Scutari, Jean-Baptiste Denis

6

Theory and Algorithms for Bayesian Networks

6.1 Conditional Independence and Graphical Separation

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