Thompson The Nature of Statistical Evidence

1. Auflage 2007
ISBN: 978-0-387-40054-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 189, 152 Seiten

Reihe: Lecture Notes in Statistics

The purpose of this book is to discuss whether statistical methods make sense. The present volume begins the task of providing interpretations and explanations of several theories of statistical evidence. It should be relevant to anyone interested in the logic of experimental science. Have we achieved a true Foundation of Statistics? We have made the link with one widely accepted view of science and we have explained the senses in which Bayesian statistics and p-values allow us to draw conclusions. This book has substantial implications for all users of Statistical methods.

Autoren/Hrsg.

Thompson, Bill

Inhaltsverzeichnis

1;Contents;5
2;Overview;10
3;The Context;15
3.1;Mathematics and Its Applications;16
3.1.1;2.1. Axiomatic Method and Mathematics;16
3.1.2;2.2. Prepositional Calculus as an Axiomatic System;19
3.1.3;2.3. The Euclidean Geometry Paradigm^;20
3.1.4;2.4. Formal Science and Applied Mathematics;22
3.1.5;Notes on the Literature;24
3.2;The Evolution of Natural Scientists and Their Theories;25
3.2.1;3.1. Background;25
3.2.2;3.2. "Prediction = Science"?;28
3.2.3;3.3. External Aspects of Science;31
3.2.4;3.4. Conclusion Theory;36
3.3;Law and Learning;40
3.3.1;4.1. The Law;40
3.3.2;4.2. Learning Theory;42
4;Interpreting Probability;45
4.1;Introduction to Probability;46
4.1.1;5.1. The Axiomatic Theory;47
4.1.2;5.2. Interpreting the Axiomatic Theory;52
4.1.3;5.3. Enumerative Probability;54
4.1.4;5.4. Frequency Probability;55
4.1.5;5.5. Propensity Probability—"Tendency To Happen";56
4.2;The Fair Betting Utility Interpretation of Probability;59
4.2.1;6.1. Probability as Personal Price;59
4.2.2;6.2. Probability as Personal Degree of Belief;63
4.2.3;6.3. Conditional Subjective Probability;64
4.3;Attitudes Toward Chance;66
4.3.1;7.1. Indeterminism and Chance;66
4.3.2;7.2. The Location of Probability—Mind or Matter?;67
4.3.3;7.3. Equally Likely;68
4.3.4;7.4. Frequency and the Law of Large Numbers;72
4.3.5;7.5. The Single Instance;74
4.3.6;7.6. Locations of Some Kinds of Probabilities;75
5;Statistical Models of Induction;77
5.1;A Framework for Statistical Evidence;78
5.1.1;8.1. Introduction;78
5.1.2;8.2. What Is an Experiment?;79
5.1.3;8.3. Ey{ E, y) Does Not Exist;80
5.1.4;8.4. The Fitted Parameter Model;81
5.1.5;8.5. Interlaboratory Experimentation;82
5.1.6;8.6. Conclusion;86
5.2;A Critique of Bayesian Inference;87
5.2.1;9.1. Randomness Needs Explaining;87
5.2.2;9.2. How to Adjust Your Belief;89
5.2.3;9.3. The Economic Approach to Group BeHef;91
5.2.4;9.4. Objective Bayesian Statistics;97
5.3;The Long-Run Consequence of Behavior;100
5.3.1;10.1. Decision Theory;100
5.3.2;10.2. The Accept-Reject Theory;101
5.3.3;10.3. Frequency Interpretation of Confidence Intervals;102
5.4;A Critique of p-Values;105
5.4.1;11.1. The Context;105
5.4.2;11.2. Simple Hypotheses;107
5.4.3;11.3. Composite Hypotheses;111
5.4.4;11.4. Test of a Direction;113
5.4.5;11.5. Asymptotic Considerations;115
5.4.6;11.6. Intuitive Test Statistics;116
5.4.7;11.7. Discussion;118
5.5;The Nature of Statistical Evidence;119
5.5.1;12.1. Introduction;119
5.5.2;12.2. Birnbaum's Theorem;120
5.5.3;12.3. Counterexamples;123
5.6;The Science of Statistics;125
5.6.1;13.1. Meanings of " Science";125
5.6.2;13.2. Concepts of Statistics;127
5.6.3;13.3. Is Statistics a Science?;127
5.7;Comparison of Evidential Theories;129
5.7.1;14.1. Evidential Models and Their Criteria;129
5.7.2;14.2. Two Interpretations of the Mathematics of Testing Are Needed;129
5.7.3;14.3. Evidential Meaning;130
5.7.4;14.4. Comparison of Bayesian, Likelihood, and " Show- Me" Evidence;130
5.7.5;14.5. An Example—Probability Evidence and the Law;133
5.8;Appendix A Deductive Logic;136
5.8.1;A. l. The Propositional Calculus;136
5.8.2;A.2. Truth Tables;138
5.8.3;A. 3. Deductive Arguments and Conditional Statements;139
5.8.4;A.4. Critique of Classical Logic;142
5.8.5;A. 5. Many-Valued Logic;143
5.8.6;Notes on the Literature;145
6;Author Index;151
7;Subject Index;153