Bayesian Networks

With Examples in R

Marco Scutari, Jean-Baptiste Denis

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Print ISBN:
  9780367366513
• Edition: 2
• eBook ISBN:
  9781000410396
• Topic: Mathematics
• Subtopic: Computer Science General
• Index: Mathematics

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.

Online supplementary materials include the data sets and the code used in the book, which will all be made available from https://www.bnlearn.com/book-crc-2ed/

1 The Discrete Case: Multinomial Bayesian Networks

DOI: 10.1201/9780429347436-1

In this chapter we will introduce the fundamental ideas behind Bayesian networks (BNs) and their interpretation using a hypothetical survey on the usage of different means of transport. We will focus on modelling discrete data, leaving continuous data to Chapter 2 and more complex data types to Chapters 3 and 5.

1.1 Introductory Example: Train-Use Survey

Consider a simple, hypothetical survey whose aim is to investigate the usage patterns of different means of transport, with a focus on cars and trains. Such surveys are used to assess customer satisfaction across different social groups, to evaluate public policies and to improve urban planning. Some real-world examples can be found, for instance, in Kenett et al. (2012).

In our current example we will examine, for each individual, the following six discrete variables (labels used in computations and figures are reported in parenthesis):

• Age (A): the age, recorded as young (young) for individuals below 30 years old, adult (adult) for individuals between 30 and 60 years old, and old (old) for people older than 60.
• Sex (S): the biological sex, recorded as male (M) or female (F).
• Education (E): the highest level of education or training successfully completed, recorded as up to high school (high) or university degree (uni).
• Occupation (O): whether the individual is an employee (emp) or a self-employed (self) worker.
• Residence (R): the size of the city the individual lives in, recorded as either small (small) or big (big).
• Travel (T): the means of transport favoured by the individual, recorded either as car (car), train (train) or other (other).

In the scope of this survey, each variable falls into one of three groups. Age and Sex are demographic indicators. In other words, they are intrinsic characteristics of the individual; they may result in different patterns of behaviour but are not influenced by the individual himself. On the other hand, the opposite is true for Education, Occupation and Residence. These variables are socioeconomic indicators and describe the individual's position in society. Therefore, they provide a rough description of the individual's expected lifestyle; for example, they may characterise his spending habits and his work schedule. The last variable, Travel, is the target of the survey, the quantity of interest whose behaviour is under investigation.

1.2 Graphical Representation

The nature of the variables recorded in the survey, and more in general of the three categories they belong to, suggests how they may be related with each other. Some of these relationships will be direct, while others will be mediated by one or more variables (indirect).

Both kinds of relationships can be represented effectively and intuitively by means of a directed graph, which is one of the two fundamental entities characterising a BN. Each node in the graph corresponds to one of the variables in the survey. In fact, they are usually referred to interchangeably in the literature. Therefore, the graph produced from this example will contain six nodes, labelled after the variables (A, S, E, O, R and T). Direct dependence relationships are represented as arcs between pairs of variables (e.g., $\mathrm{A}\to \mathrm{E}$ means that E depends on A). The node at the tail of the arc is called the parent, while that at the head (where the arrow is) is called the child. Indirect dependence relationships are not explicitly represented. However, they can be read from the graph as sequences of arcs leading from one variable to the other through one or more mediating variables (e.g., the combination of $\mathrm{A}\to \mathrm{E}$ and $\mathrm{E}\to \mathrm{R}$ means that R depends on A through E). Such sequences of arcs are said to form a path leading from one variable to the other; these two variables must be ...

Table of contents

• 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
• 2 The Continuous Case: Gaussian Bayesian Networks
• 3 The Mixed Case: Conditional Gaussian Bayesian Networks
• 4 Time Series: Dynamic Bayesian Networks
• 5 More Complex Cases: General Bayesian Networks
• 6 Theory and Algorithms for Bayesian Networks
• 7 Software for Bayesian Networks
• 8 Real-World Applications of Bayesian Networks
• A Graph Theory
• B Probability Distributions
• C A Note about Bayesian Networks
• Glossary
• Solutions
• Bibliography
• Index