The Nature of Statistical Evidence Book

Overview     1
The Context
Mathematics and Its Applications     9
Axiomatic Method and Mathematics     9
Prepositional Calculus as an Axiomatic System     12
The Euclidean Geometry Paradigm     13
Formal Science and Applied Mathematics     15
Notes on the Literature     17
The Evolution of Natural Scientists and Their Theories     18
Background     18
"Prediction = Science"?     21
External Aspects of Science     24
Conclusion Theory     29
Law and Learning     33
The Law     33
Learning Theory     35
Interpreting Probability
Introduction to Probability     41
The Axiomatic Theory     42
Interpreting the Axiomatic Theory     47
Enumerative Probability     49
Frequency Probability     50
Propensity Probability-"Tendency to Happen"     51
The Fair Betting Utility Interpretation of Probability     54
Probability as Personal Price     54
Probability as Personal Degree of Belief     58
Conditional Subjective Probability     59
Attitudes Toward Chance     61
Indeterminismand Chance     61
The Location of Probability-Mind or Matter?     62
Equally Likely     63
Frequency and the Law of Large Numbers     67
The Single Instance     69
Locations of Some Kinds of Probabilities     70
Statistical Models of Induction
A Framework for Statistical Evidence     75
Introduction     75
What Is an Experiment?     76
E[subscript v](E, y) Does Not Exist     77
The Fitted Parameter Model     78
Interlaboratory Experimentation     79
Conclusion     83
A Critique of Bayesian Inference     84
Randomness Needs Explaining     84
How to Adjust Your Belief     86
The Economic Approach to Group Belief     88
Objective Bayesian Statistics     94
The Long-Run Consequence of Behavior     97
Decision Theory     97
The Accept-Reject Theory     98
Frequency Interpretation of Confidence Intervals     99
A Critique of p-Values     102
The Context     102
Simple Hypotheses     104
Composite Hypotheses     108
Test of a Direction     110
Asymptotic Considerations     112
Intuitive Test Statistics     113
Discussion     115
The Nature of Statistical Evidence     116
Introduction     116
Birnbaum's Theorem     117
Counterexamples     120
The Science of Statistics     122
Meanings of "Science"     122
Concepts of Statistics     124
Is Statistics a Science?     124
Comparison of Evidential Theories     126
Evidential Models and Their Criteria     126
Two Interpretations of the Mathematics of Testing Are Needed     126
Evidential Meaning     127
Comparison of Bayesian, Likelihood, and "Show-Me" Evidence     127
An Example-Probability Evidence and the Law     130
Deductive Logic     133
The Prepositional Calculus     133
Truth Tables     135
Deductive Arguments and Conditional Statements     136
Critique of Classical Logic     139
Many-Valued Logic     140
Notes on the Literature     142
References     143
Author Index     149
Subject Index     151