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해외주문 [POD] Model Selection and Multi-Model Inference A Practical Information-Theoretic Approach

0002/E 2002. Corr. 3rd | Hardcover
Burnham, Kenneth P. , Anderson, David R. 지음 | Springer | 2003년 12월 04일
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상품상세정보
ISBN 9780387953649(0387953647)
쪽수 496쪽
언어 English
크기 161(W) X 240(H) X 28(T) (mm)
0002/E 2002. Corr. 3rd
제본형태 Hardcover
삽화유무 삽화있음
총권수 1권
리딩지수 Level Scholarly/Undergraduate

책소개

이 책이 속한 분야

The second edition of this book is unique in that it focuses on methods for making formal statistical inference from all the models in an a priori set (Multi-Model Inference). A philosophy is presented for model-based data analysis and a general strategy outlined for the analysis of empirical data. The book invites increased attention on a priori science hypotheses and modeling.Kullback-Leibler Information represents a fundamental quantity in science and is Hirotugu Akaike's basis for model selection. The maximized log-likelihood function can be bias-corrected as an estimator of expected, relative Kullback-Leibler information. This leads to Akaike's Information Criterion (AIC) and various extensions. These methods are relatively simple and easy to use in practice, but based on deep statistical theory. The information theoretic approaches provide a unified and rigorous theory, an extension of likelihood theory, an important application of information theory, and are objective and practical to employ across a very wide class of empirical problems.The book presents several new ways to incorporate model selection uncertainty into parameter estimates and estimates of precision. An array of challenging examples is given to illustrate various technical issues.This is an applied book written primarily for biologists and statisticians wanting to make inferences from multiple models and is suitable as a graduate text or as a reference for professional analysts.
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목차

Prefacep. vii
About the Authorsp. xxi
Glossaryp. xxiii
Introductionp. 1
Objectives of the Bookp. 1
Background Materialp. 5
Inference from Data, Given a Modelp. 5
Likelihood and Least Squares Theoryp. 6
The Critical Issue: "What Is the Best Model to Use?"p. 13
Science Inputs: Formulation of the Set of Candidate Modelsp. 15
Models Versus Full Realityp. 20
An Ideal Approximating Modelp. 22
Model Fundamentals and Notationp. 23
Truth or Full Reality fp. 23
Approximating Models g[subscript i](x [theta])p. 23
The Kullback-Leibler Best Model g[subscript i](x [theta subscript o])p. 25
Estimated Models g[subscript i](x [theta])p. 25
Generating Modelsp. 26
Global Modelp. 26
Overview of Stochastic Models in the Biological Sciencesp. 27
Inference and the Principle of Parsimonyp. 29
Avoid Overfitting to Achieve a Good Model Fitp. 29
The Principle of Parsimonyp. 31
Model Selection Methodsp. 35
Data Dredging, Overanalysis of Data, and Spurious Effectsp. 37
Overanalysis of Datap. 38
Some Trendsp. 40
Model Selection Biasp. 43
Model Selection Uncertaintyp. 45
Summaryp. 47
Information and Likelihood Theory: A Basis for Model Selection and Inferencep. 49
Kullback--Leibler Information or Distance Between Two Modelsp. 50
Examples of Kullback--Leibler Distancep. 54
Truth, f, Drops Out as a Constantp. 58
Akaike's Information Criterion: 1973p. 60
Takeuchi's Information Criterion: 1976p. 65
Second-Order Information Criterion: 1978p. 66
Modification of Information Criterion for Overdispersed Count Datap. 67
AIC Differences, [Delta subscript i]p. 70
A Useful Analogyp. 72
Likelihood of a Model, L(g[subscript i]p. 74
Akaike Weights, [omega subscript i]p. 75
Basic Formulap. 75
An Extensionp. 76
Evidence Ratiosp. 77
Important Analysis Detailsp. 80
AIC Cannot Be Used to Compare Models of Different Data Setsp. 80
Order Not Important in Computing AIC Valuesp. 81
Transformations of the Response Variablep. 81
Regression Models with Differing Error Structuresp. 82
Do Not Mix Null Hypothesis Testing with Information-Theoretic Criteriap. 83
Null Hypothesis Testing Is Still Important in Strict Experimentsp. 83
Information-Theoretic Criteria Are Not a "Test"p. 84
Exploratory Data Analysisp. 84
Some History and Further Insightsp. 85
Entropyp. 86
A Heuristic Interpretationp. 87
More on Interpreting Information-Theoretic Criteriap. 87
Nonnested Modelsp. 88
Further Insightsp. 89
Bootstrap Methods and Model Selection Frequencies [pi subscript i]p. 90
Introductionp. 91
The Bootstrap in Model Selection: The Basic Ideap. 93
Return to Flather's Modelsp. 94
Summaryp. 96
Basic Use of the Information-Theoretic Approachp. 98
Introductionp. 98
Example 1: Cement Hardening Datap. 100
Set of Candidate Modelsp. 101
Some Results and Comparisonsp. 102
A Summaryp. 106
Example 2: Time Distribution of an Insecticide Added to a Simulated Ecosystemp. 106
Set of Candidate Modelsp. 108
Some Resultsp. 110
Example 3: Nestling Starlingsp. 111
Experimental Scenariop. 112
Monte Carlo Datap. 113
Set of Candidate Modelsp. 113
Data Analysis Resultsp. 117
Further Insights into the First Fourteen Nested Modelsp. 120
Hypothesis Testing and Information-Theoretic Approaches Have Different Selection Frequenciesp. 121
Further Insights Following Final Model Selectionp. 124
Why Not Always Use the Global Model for Inference?p. 125
Example 4: Sage Grouse Survivalp. 126
Introductionp. 126
Set of Candidate Modelsp. 127
Model Selectionp. 129
Hypothesis Tests for Year-Dependent Survival Probabilitiesp. 131
Hypothesis Testing Versus AIC in Model Selectionp. 132
A Class of Intermediate Modelsp. 134
Example 5: Resource Utilization of Anolis Lizardsp. 137
Set of Candidate Modelsp. 138
Comments on Analytic Methodp. 138
Some Tentative Resultsp. 139
Example 6: Sakamoto et al.'s (1986) Simulated Datap. 141
Example 7: Models of Fish Growthp. 142
Summaryp. 143
Formal Inference From More Than One Model: Multimodel Inference (MMI)p. 149
Introduction to Multimodel Inferencep. 149
Model Averagingp. 150
Predictionp. 150
Averaging Across Model Parametersp. 151
Model Selection Uncertaintyp. 153
Concepts of Parameter Estimation and Model Selection Uncertaintyp. 155
Including Model Selection Uncertainty in Estimator Sampling Variancep. 158
Unconditional Confidence Intervalsp. 164
Estimating the Relative Importance of Variablesp. 167
Confidence Set for the K-L Best Modelp. 169
Introductionp. 169
[Delta subscript i], Model Selection Probabilities, and the Bootstrapp. 171
Model Redundancyp. 173
Recommendationsp. 176
Cement Datap. 177
Pine Wood Datap. 183
The Durban Storm Datap. 187
Models Consideredp. 188
Consideration of Model Fitp. 190
Confidence Intervals on Predicted Storm Probabilityp. 191
Comparisons of Estimator Precisionp. 193
Flour Beetle Mortality: A Logistic Regression Examplep. 195
Publication of Research Resultsp. 201
Summaryp. 203
Monte Carlo Insights and Extended Examplesp. 206
Introductionp. 206
Survival Modelsp. 207
A Chain Binomial Survival Modelp. 207
An Examplep. 210
An Extended Survival Modelp. 215
Model Selection if Sample Size Is Huge, or Truth Knownp. 219
A Further Chain Binomial Modelp. 221
Examples and Ideas Illustrated with Linear Regressionp. 224
All-Subsets Selection: A GPA Examplep. 225
A Monte Carlo Extension of the GPA Examplep. 229
An Improved Set of GPA Prediction Modelsp. 235
More Monte Carlo Resultsp. 238
Linear Regression and Variable Selectionp. 244
Discussionp. 248
Estimation of Density from Line Transect Samplingp. 255
Density Estimation Backgroundp. 255
Line Transect Sampling of Kangaroos at Wallaby Creekp. 256
Analysis of Wallaby Creek Datap. 256
Bootstrap Analysisp. 258
Confidence Interval on Dp. 258
Bootstrap Samples: 1,000 Versus 10,000p. 260
Bootstrap Versus Akaike Weights: A Lesson on QAIC[subscript c]p. 261
Summaryp. 264
Advanced Issues and Deeper Insightsp. 267
Introductionp. 267
An Example with 13 Predictor Variables and 8,191 Modelsp. 268
Body Fat Datap. 268
The Global Modelp. 269
Classical Stepwise Selectionp. 269
Model Selection Uncertainty for AIC[subscript c] and BICp. 271
An A Priori Approachp. 274
Bootstrap Evaluation of Model Uncertaintyp. 276
Monte Carlo Simulationsp. 279
Summary Messagesp. 281
Overview of Model Selection Criteriap. 284
Criteria That Are Estimates of K-L Informationp. 284
Criteria That Are Consistent for Kp. 286
Contrastsp. 288
Consistent Selection in Practice: Quasi-true Modelsp. 289
Contrasting AIC and BICp. 293
A Heuristic Derivation of BICp. 293
A K-L-Based Conceptual Comparison of AIC and BICp. 295
Performance Comparisonp. 298
Exact Bayesian Model Selection Formulasp. 301
Akaike Weights as Bayesian Posterior Model Probabilitiesp. 302
Goodness-of-Fit and Overdispersion Revisitedp. 305
Overdispersion c and Goodness-of-Fit: A General Strategyp. 305
Overdispersion Modeling: More Than One cp. 307
Model Goodness-of-Fit After Selectionp. 309
AIC and Random Coefficient Modelsp. 310
Basic Concepts and Marginal Likelihood Approachp. 310
A Shrinkage Approach to AIC and Random Effectsp. 313
On Extensionsp. 316
Selection When Probability Distributions Differ by Modelp. 317
Keep All the Partsp. 317
A Normal Versus Log-Normal Examplep. 318
Comparing Across Several Distributions: An Examplep. 320
Lessons from the Literature and Other Mattersp. 323
Use AIC[subscript c], Not AIC, with Small Sample Sizesp. 323
Use AIC[subscript c], Not AIC, When K Is Largep. 325
When Is AIC[subscript c] Suitable: A Gamma Distribution Examplep. 326
Inference from a Less Than Best Modelp. 328
Are Parameters Real?p. 330
Sample Size Is Often Not a Simple Issuep. 332
Judgment Has a Rolep. 333
Tidbits About AICp. 334
Irrelevance of Between-Sample Variation of AICp. 334
The G-Statistic and K-L Informationp. 336
AIC Versus Hypothesis Testing: Results Can Be Very Differentp. 337
A Subtle Model Selection Bias Issuep. 339
The Dimensional Unit of AICp. 340
AIC and Finite Mixture Modelsp. 342
Unconditional Variancep. 344
A Baseline for [omega subscript +](i)p. 345
Summaryp. 347
Statistical Theory and Numerical Resultsp. 352
Useful Preliminariesp. 352
A General Derivation of AICp. 362
General K-L--Based Model Selection: TICp. 371
Analytical Computation of TICp. 371
Bootstrap Estimation of TICp. 372
AIC[subscript c]: A Second-Order Improvementp. 374
Derivation of AIC[subscript c]p. 374
Lack of Uniqueness of AIC[subscript c]p. 379
Derivation of AIC for the Exponential Family of Distributionsp. 380
Evaluation of tr(J([theta subscript o])[I([theta subscript o]) superscript -1]) and Its Estimatorp. 384
Comparison of AIC Versus TIC in a Very Simple Settingp. 385
Evaluation Under Logistic Regressionp. 390
Evaluation Under Multinomially Distributed Count Datap. 397
Evaluation Under Poisson-Distributed Datap. 405
Evaluation for Fixed-Effects Normality-Based Linear Modelsp. 406
Additional Results and Considerationsp. 412
Selection Simulation for Nested Modelsp. 412
Simulation of the Distribution of [Delta subscript p]p. 415
Does AIC Overfit?p. 417
Can Selection Be Improved Based on All the [Delta subscript i]?p. 419
Linear Regression, AIC, and Mean Square Errorp. 421
AIC[subscript c] and Models for Multivariate Datap. 424
There Is No True TIC[subscript c]p. 426
Kullback--Leibler Information Relationship to the Fisher Information Matrixp. 426
Entropy and Jaynes Maxent Principlep. 427
Akaike Weights [omega subscript i] Versus Selection Probabilities [pi subscript i]p. 428
Kullback--Leibler Information Is Always [greater than or equal] 0p. 429
Summaryp. 434
Summaryp. 437
The Scientific Question and the Collection of Datap. 439
Actual Thinking and A Priori Modelingp. 440
The Basis for Objective Model Selectionp. 442
The Principle of Parsimonyp. 443
Information Criteria as Estimates of Expected Relative Kullback--Leibler Informationp. 444
Ranking Alternative Modelsp. 446
Scaling Alternative Modelsp. 447
MMI: Inference Based on Model Averagingp. 448
MMI: Model Selection Uncertaintyp. 449
MMI: Relative Importance of Predictor Variablesp. 451
More on Inferencesp. 451
Final Thoughtsp. 454
Referencesp. 455
Indexp. 485
Table of Contents provided by Syndetics. All Rights Reserved.

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