Box / Leonard / Wu Scientific Inference, Data Analysis, and Robustness

Proceedings of a Conference Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, November 4-6, 1981
1. Auflage 2014
ISBN: 978-1-4832-5939-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 316 Seiten, Web PDF

Mathematics Research Center Symposium: Scientific Inference, Data Analysis, and Robustness focuses on the philosophy of statistical modeling, including model robust inference and analysis of data sets. The selection first elaborates on pivotal inference and the conditional view of robustness and some philosophies of inference and modeling, including ideas on modeling, significance testing, and scientific discovery. The book then ponders on parametric empirical Bayes confidence intervals, ecumenism in statistics, and frequency properties of Bayes rules. Discussions focus on consistency of Bayes rules, scientific method and the human brain, and statistical estimation and criticism. The book takes a look at the purposes and limitations of data analysis, likelihood, shape, and adaptive inference, statistical inference and measurement of entropy, and the robustness of a hierarchical model for multinomials and contingency tables. Topics include numerical results for contingency tables and robustness, multinomials, flattening constants, and mixed Dirichlet priors, entropy and likelihood, and test as measurement of entropy. The selection is a valuable reference for researchers interested in robust inference and analysis of data sets.

Autoren/Hrsg.

Box, G. E. P.

Leonard, Tom

Wu, Chien-Fu

Inhaltsverzeichnis

1;Front Cover;1
2;Scientific Inference, Data Analysis, and Robustness;4
3;Copyright Page;5
4;Table of Contents;6
5;Contributors;8
6;Foreword;10
7;Preface;12
8;Chapter 1. Pivotal Inference and the Conditional View of Robustness (Why have we for so long managed with normality assumptions?);14
8.1;0 . SUMMARY;14
9;Chapter 2. Some Philosophies of Inference and Modelling;22
9.1;SECTION 1: INTRODUCTION;22
9.2;SECTION 2: SESSIONS 1 TO 3 WITH FURTHER IDEAS ON MODELLING, SIGNIFICANCE TESTING AND SCIENTIFIC DISCOVERY;22
9.3;SECTION 3: REVIEW OF SESSIONS 4-13;30
9.4;SECTION 4: REVIEW OF CLOSING SESSION;34
9.5;SECTION 5: FINAL WORD;34
9.6;REFERENCES;36
10;Chapter 3. Parametric Empirical Bayes Confidence Intervals;38
10.1;I. INTRODUCTION;38
10.2;2. EMPIRICAL BAYES INFERENCE AND CONFIDENCE INTERVALS;42
10.3;3. EB CONFIDENCE INTERVALS FOR 18 BASEBALL BATTERS;44
10.4;4. DERIVATION OF RULES CONSIDERED;53
10.5;5. EB CONFIDENCE INTERVALS;56
10.6;6. CONCLUSION;58
10.7;REFERENCES;61
11;Chapter 4. An Apology for Ecumenism in Statistics;64
11.1;1. SOME QUESTIONABLE SIMPLIFICATIONS;65
11.2;2. SCIENTIFIC METHOD AND THE HUMAN BRAIN;67
11.3;3. THE THEORY - PRACTICE ITERATION;70
11.4;4. STATISTICAL ESTIMATION AND CRITICISM;72
11.5;5. SOME OBJECTIONS CONSIDERED;80
11.6;CONCLUSION;94
11.7;REFERENCES;94
12;Chapter 5. Can Frequentist Inferences Be Very Wrong? A Conditional "Yes";98
12.1;1. INTRODUCTION;98
12.2;2. Likelihood Inference;101
12.3;3. Data-based Transformation; Box-Cox Revisited Again;108
12.4;4. Randomized Designs and Their Analyses;111
12.5;5. Robust Estimation;113
12.6;REFERENCES;115
13;Chapter 6. Frequency Properties of Bayes Rules;118
13.1;ABSTRACT;118
13.2;1. The "What if" Method;118
13.3;2. Consistency of Bayes Rules;120
13.4;3. Some Open Problems;126
13.5;REFERENCES;127
14;Chapter 7. Purposes and Limitations of Data Analysis;130
14.1;1. INTRODUCTION;130
14.2;2. TECHNICAL VS. FUNCTIONAL STATISTICS;131
14.3;3. RECOGNIZING STRUCTURE;132
14.4;4. VARIETIES OF CONFIRMATORY ANALYSIS;135
14.5;5. ROBUSTNESS AND PRIOR INFORMATION;139
14.6;6. QUALITY EVALUATION;144
14.7;7. IMPLICATIONS;145
14.8;REFERENCES;146
15;Chapter 8. Data Description;148
15.1;ABSTRACT;148
15.2;INTRODUCTION;148
15.3;REFERENCES;163
16;Chapter 9. Likelihood, Shape, and Adaptive Inference;166
16.1;1. INTRODUCTION;166
16.2;2. DEFINITIONS;168
16.3;3. RESULTS;169
16.4;4. DISCUSSION;173
16.5;REFERENCES;176
17;Chapter 10. Statistical Inference and Measurement of Entropy;178
17.1;1. INTRODUCTION;178
17.2;2. ENTROPY AND LIKELIHOOD;180
17.3;3. TEST AS MEASUREMENT OF ENTROPY;181
17.4;4. P-VALUE AND AIC;185
17.5;5. MODEL SELECTION AND BAYESIAN MODELING;189
17.6;6. MEASUREMENT OF ENTROPY IN ACTION;192
17.7;ACKNOWLEDGEMENTS;194
17.8;REFERENCES;200
18;Chapter 11. The Robustness of a Hierarchical Model for Multinomials and Contingency Tables;204
18.1;1. INTRODUCTION: PHILOSOPHICAL MATTERS;204
18.2;2. MULTINOMIALS, FLATTENING CONSTANTS, AND MIXED DIRICHLET PRIORS;207
18.3;3. CONTINGENCY TABLES;211
18.4;4. NUMERICAL RESULTS FOR CONTINGENCY TABLES, AND ROBUSTNESS;213
18.5;5. THE TYPE II LIKELIHOOD RATIO;214
18.6;6. WHEN CAN ONE REJECT THE SYMMETRICAL DIRICHLET PRIORS FOR MULTINOMIALS?;215
18.7;7. SCIENTIFIC INDUCTION, UNIVERSAL AND PREDICTIVE;218
18.8;REFERENCES;221
19;Chapter 12. A Case Study of the Robustness of Bayesian Methods of Inference: Estimating the Total in a Finite Population Using Transformations to Normality;226
19.1;1. PROLOGUE-THE PRACTICAL INTERPRETATION OF INTERVAL ESTIMATES AS BAYES INTERVALS;226
19.2;2. THE ROBUSTNESS OF BAYESIAN METHODS;227
19.3;3. SAMPLE 1 — INITIAL ANALYSIS;232
19.4;4. SAMPLE 1 — EXTENDED ANALYSES;238
19.5;5. SAMPLE 2;242
19.6;6. NEED TO SPECIFY CRITICAL PRIOR INFORMATION;247
19.7;7. GOOD FITS AND SPECIFIED EXTREME VALUES ARE NOT ENOUGH WITH SUCH DATA;250
19.8;8. ROBUST QUESTIONS AND SAMPLES OBVIATE THE NEED FOR STRONG PRIOR INFORMATION;252
19.9;APPENDIX;254
19.10;REFERENCES;256
19.11;ACKNOWLEDGEMENTS;257
20;Chapter 13. Estimation of Variance of the Ratio Estimator: An Empirical Study;258
20.1;1. INTRODUCTION;258
20.2;2. RATIO ESTIMATOR AND ITS VARIANCE;260
20.3;3. VARIANCE ESTIMATORS UNDER STUDY;261
20.4;4. POPULATIONS UNDER STUDY;264
20.5;5. RESULTS;272
20.6;6. CONCLUSIONS AND FURTHER REMARKS;285
20.7;REFERENCES;289
21;Chapter 14. Autocorrelation-robust Design of Experiments;292
21.1;1. BACKGROUND;292
21.2;2. ONE DIMENSION: ANALYSIS;293
21.3;3. STATIONARY BINARY PROCESSES IN ONE DIMENSION;295
21.4;4. HIGHER DIMENSIONS;302
21.5;5. PSEUDO-RANDOM PATTERNS;309
21.6;REFERENCES;311
22;Index;314