Bayesian Networks: With Examples in R
Preface xiii
1 The Discrete Case: Multinomial Bayesian Networks 1
1.1 Introductory Example: Train Use Survey . . . . . . . . . . . 1
1.2 Graphical Representation . . . . . . . . . . . . . . . . . . . . 2
1.3 Probabilistic Representation . . . . . . . . . . . . . . . . . . 7
1.4 Estimating the Parameters: Conditional Probability Tables . 11
1.5 Learning the DAG Structure: Tests and Scores . . . . . . . . 14
1.5.1 Conditional Independence Tests . . . . . . . . . . . . . 15
1.5.2 Network Scores . . . . . . . . . . . . . . . . . . . . . . 17
1.6 Using Discrete BNs . . . . . . . . . . . . . . . . . . . . . . . 20
1.6.1 Using the DAG Structure . . . . . . . . . . . . . . . . 20
1.6.2 Using the Conditional Probability Tables . . . . . . . 23
1.6.2.1 Exact Inference . . . . . . . . . . . . . . . . 23
1.6.2.2 Approximate Inference . . . . . . . . . . . . 27
1.7 Plotting BNs . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.7.1 Plotting DAGs . . . . . . . . . . . . . . . . . . . . . . 29
1.7.2 Plotting Conditional Probability Distributions . . . . 31
1.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 The Continuous Case: Gaussian Bayesian Networks 37
2.1 Introductory Example: Crop Analysis . . . . . . . . . . . . . 37
2.2 Graphical Representation . . . . . . . . . . . . . . . . . . . . 38
2.3 Probabilistic Representation . . . . . . . . . . . . . . . . . . 42
2.4 Estimating the Parameters: Correlation Coefficients . . . . . 46
2.5 Learning the DAG Structure: Tests and Scores . . . . . . . . 49
2.5.1 Conditional Independence Tests . . . . . . . . . . . . . 49
2.5.2 Network Scores . . . . . . . . . . . . . . . . . . . . . . 52
2.6 Using Gaussian Bayesian Networks . . . . . . . . . . . . . . 52
2.6.1 Exact Inference . . . . . . . . . . . . . . . . . . . . . . 53
2.6.2 Approximate Inference . . . . . . . . . . . . . . . . . . 54
2.7 Plotting Gaussian Bayesian Networks . . . . . . . . . . . . . 57
2.7.1 Plotting DAGs . . . . . . . . . . . . . . . . . . . . . . 57
2.7.2 Plotting Conditional Probability Distributions . . . .