2nd Edition

Bayesian Networks With Examples in R

By Marco Scutari, Jean-Baptiste Denis Copyright 2022
    274 Pages
    by Chapman & Hall

    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/

    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                    

     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          



    Marco Scutari is a Senior Lecturer at Istituto Dalle Molle di Studisull'Intelligenza Artificiale (IDSIA), Switzerland. He has held positions in Statistics, Statistical Genetics and Machine Learning in the UK and Switzerland since completing his Ph.D. in Statistics in 2011. His research focuses on the theory of Bayesian networks and their applications to biological and clinical data, as well as statistical computing and software engineering.

    Jean-Baptiste Denis was formerly appointed as a statistician and modeller at the "Mathematics and Applied Informatics from Genome to Environment" unit of the French National Research Institute for Agriculture, Food and Environment. His main research interests were the modelling of two-way tables and Bayesian approaches, especially applied to genotype-by-environment interactions and microbiological food safety.

    "The book has a practice-oriented, hands-on approach with R codes and outputs, clear examples, relevant exercises to elucidate the main concepts (with solutions included at the end). [...] Statisticians, data scientists and other researchers new to Bayesian networks might also find it valuable and interesting."
    -Anikó Lovik in ISCB News, June 2022

    Praise for the first edition:

    "… an excellent introduction to Bayesian networks with detailed user-friendly examples and computer-aided illustrations. I enjoyed reading Bayesian Networks: With Examples in R and think that the book will serve very well as an introductory textbook for graduate students, non-statisticians, and practitioners in Bayesian networks and the related areas."
    Biometrics, September 2015

    "Several excellent books about learning and reasoning with Bayesian networks are available and Bayesian Networks: With Examples in R provides a useful addition to this list. The book is usually easy to read, rich in examples that are described in great detail, and also provides several exercises with solutions that can be valuable to students. The book also provides an introduction to topics that are not covered in detail in existing books … . It also provides a good list of search algorithms for learning Bayesian network structures. But the major strength of the book is the simplicity that makes it particularly suitable to students with sufficient background in probability and statistical theory, particularly Bayesian statistics."
    Journal of the American Statistical Association, June 2015