Graphical models in applied multivariate statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chicester [u. a.]
Wiley
1991
|
| Edition: | Reprint. |
| Series: | Wiley series in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 426 - 435 |
| Physical Description: | XIV, 448 S. graph. Darst. |
| ISBN: | 0471917508 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Graphical models in applied multivariate statistics
Autor: Whittaker, Joe
Jahr: 1991
Contents v Contents Preface ix Glossary xiii 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 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 2.5 Three Dimensional Bernoulli Distribution 42 2.6 The Normal Distribution 47 2.7 Exercises 51 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 3.7 Exercises 82 Information Divergence 86 4.1 Kullback-Leibler Information Divergence 87 4.2 Divergence: a Heuristic Derivation 91 4.3 Properties of Information Divergence 94
VI Contents 4.4 Independence and Information Proper 99 4.5 Information in an Independence Graph 105 4.6 Divergence and Collapsibility 108 4.7 Iterative Proportional Fitting 112 4.8 Exercises 117 5 The Inverse Variance 120 5.1 Random Vectors, Expectation and Covariance 121 5.2 Linear Least Squares Prediction 125 5.3 Properties of the Predictor 128 5.4 Predicting the Mathematics Marks 132 5.5 The Partial Covariance 134 5.6 Invariance, Additivity and Recurrence 137 5.7 The Inverse Variance 141 5.8 Inverse Variance Lemma: Corollaries 143 5.9 Variance: Trace and Determinant 148 5.10 Exercises 150 6 Graphical Gaussian Models 155 6.1 Graphical Models and Modelling 156 6.2 The Multivariate Normal Distribution 158 6.3 Marginal and Conditional Distributions 162 6.4 Divergence between Normal Distributions 166 6.5 The Likelihood Function 170 6.6 Maximum Likelihood Estimates 173 6.7 Direct and Indirect Estimates 177 6.8 The Analysis of Deviance 185 6.9 Wishart, Bartlett and Mahalanobis 190 6.10 Exercises 194 7 Graphical Log-linear Models 198 7.1 The Cross-classified Multinomial Distribution 200 7.2 Log-linear Expansions and u- terms 204 7.3 Graphical Log-linear Models 207 7.4 The Likelihood Function 213 7.5 Simple Examples of MLE 217 7.6 Estimates for Conditional Independence Models 222 7.7 Partitioning the Deviance 226 7.8 Diagnostics for Log-linear Models 232 7.9 Exercises 235
Contents vii 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 269 9.1 The Partial Cross-product Ratio 270 9.2 The All Two-way Interaction Model 276 9.3 A Case Study: Rochdale 279 9.4 Exact Conditional Tests 285 9.5 Exact Tests for Graphical Models 292 9.6 Exercises 296 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 345 11.1 The CG Distribution 347 11.2 Interaction Model Formulae 352 11.3 The Likelihood Function 355 11.4 Issues in Modelling 357 11.5 Case Studies 359 11.6 Exercises 370 12 Decompositions and Decomposability 374 12.1 Factorisation 375 12.2 Partial Factorisations: Decompositions 381 12.3 Irreducible Components 384 12.4 Decomposability 388
VII] Contents 12.5 Collapsibility 394 12.6 Exercises 401 Appendices 403 A.l Computing Packages 403 A.2 Outline Answers 408 References 426 Author Index 436 Subject Index 439
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| institution | BVB |
| isbn | 0471917508 |
| language | English |
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| physical | XIV, 448 S. graph. Darst. |
| publishDate | 1991 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and mathematical statistics |
| spelling | Whittaker, Joe Verfasser aut Graphical models in applied multivariate statistics Joe Whittaker Reprint. Chicester [u. a.] Wiley 1991 XIV, 448 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Literaturverz. S. 426 - 435 Graphentheoretisches Modell (DE-588)4158055-2 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Graphentheorie (DE-588)4113782-6 s DE-604 Graphentheoretisches Modell (DE-588)4158055-2 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019136217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Whittaker, Joe Graphical models in applied multivariate statistics Graphentheoretisches Modell (DE-588)4158055-2 gnd Multivariate Analyse (DE-588)4040708-1 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4158055-2 (DE-588)4040708-1 (DE-588)4113782-6 |
| title | Graphical models in applied multivariate statistics |
| title_auth | Graphical models in applied multivariate statistics |
| title_exact_search | Graphical models in applied multivariate statistics |
| title_full | Graphical models in applied multivariate statistics Joe Whittaker |
| title_fullStr | Graphical models in applied multivariate statistics Joe Whittaker |
| title_full_unstemmed | Graphical models in applied multivariate statistics Joe Whittaker |
| title_short | Graphical models in applied multivariate statistics |
| title_sort | graphical models in applied multivariate statistics |
| topic | Graphentheoretisches Modell (DE-588)4158055-2 gnd Multivariate Analyse (DE-588)4040708-1 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphentheoretisches Modell Multivariate Analyse Graphentheorie |
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