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BK

Chichester : John Wiley & Sons, 1989

xiv, 448 s. : il.

ISBN 0-471-91750-8

000035425

Preface ix // Glossary xiii // 1 Introduction 1 // 1.1 Mathematics Marks 1 // 1.2 Infant Survival 6 // 1.3 Graphical Models and Modelling 8 // 1.4 Notational Preliminaries 14 // 1.5 Overview 18 // 2 Independence and Interaction 23 // 2.1 Independent Events 24 // 2.2 Independent Random Vectors 30 // 2.3 Mixed Derivative Measures of Interaction 35 // 2.4 The Bernoulli Distribution 38 // .5 Three Dimensional Bernoulli Distribution 42 // 2.6 The Normal Distribution 47 // .7 Exercises 51 // 3 Independence Graphs 56 // 3.1 Graph Theory . 58 // 3.2 Independence Graphs 60 // 3.3 Separation 63 // 3.4 Markov Properties 68 // 3.5 Directed Acyclic Independence Graphs 71 // 3.6 Chain Independence Graphs 77 // 9 T : 82 // 3.7 Exercises 02 // 4 Information Divergence 86 // 4.1 Kullback-Leibler Information Divergence 87 // 4.2 Divergence: a Heuristic Derivation 91 // 4 3 Properties of Information Divergence 94 // 4.4 Independence and Information Proper // 4.5 Information in an Independence Graph // 4.6 Divergence and Collapsibility // 4.7 Iterative Proportional Fitting // 4.8 Exercises // 5 The Inverse Variance // 5 1 Random Vectors, Expectation and Covariance // 5.2 Linear Least Squares Prediction // 5.3 Properties of the Predictor // 5.4 Predicting the Mathematics Marks // 5.5 The Partial Covariance // 5.6 Invariance, Additivity and Recurrence // 5.7 The Inverse Variance // 5.8 Inverse Variance Lemma: Corollaries // 5.9 Variance: Trace and Determinant // 5.10 Exercises //6 Graphical Gaussian Models // 6.1 Graphical Models and Modelling // 6.2 The Multivariate Normal Distribution // .3 Marginal and Conditional Distributions // 6.4 Divergence between Normal Distributions // 6.5 The Likelihood Function // 6.6 Maximum Likelihood Estimates // 6.7 Direct and Indirect Estimates // 6.8 The Analysis of Deviance // 6.9 Wishart, Bartlett and Mahalanobis // 6.10 Exercises //

7 Graphical Log-linear Models // The Cross-classified Multinomial Distribution // Log-linear Expansions and u-terms // Graphical Log-linear Models // The Likelihood Function // Simple Examples of MLE // Estimates for Conditional Independence Models // Partitioning the Deviance // Diagnostics for Log-linear Models // Exercises // 8 Model Selection 241 // 8.1 Issues in Model Selection 242 // 8.2 Log-linear Model Selection 246 // 8.3 Graphical Model Search Strategy 251 // 8.4 Model Selection: a Continuous Example 254 // 8.5 Model Selection: a Discrete Example 261 // 8.6 Exercises 265 // 9 Methods for Sparse Tables // The Partial Cross-product Ratio // The All Two-way Interaction Model // A Case Study: Rochdale // Exact Conditional Tests // Exact Tests for Graphical Models // Exercises // 10 Regression and Graphical Chain Models 300 // 10.1 Conditional Probability Models 304 // 10.2 Fitting Regression Models in the Joint Distribution 310 // 10.3 A Case Study: Noctuid Moth Trappings 313 // 10.4 Several blocks: A Case Study 319 // 10.5 Regression Models for Continuous Variables 322 // 10.6 Regression: Some Sampling Results 329 // 10.7 Logistic Regression 333 // 10.8 Two Case Studies with Categorical Variables 336 // 10.9 Exercises 342 // 11 Models for Mixed Variables // 11.1 The CG Distribution // 11.2 Interaction Model Formulae // 11.3 The Likelihood Function // 11.4 Issues in Modelling // 11.5 Case Studies // 11.6 Exercises // 12 Decompositions and Decomposability // 12.1 Factorisation // 12.2 Partial Factorisations: Decompositions // 12.3 Irreducible Components // 12.4 Decomposability // 12.5 Collapsibility // 12.6 Exercises // Appendices // A.1 Computing Packages // A.2 Outline Answers // References // Author Index // Subject Index