The Nature of Statistical EvidenceSpringer Science & Business Media, 21.12.2007 - 152 Seiten Our motivation for writing this book was a dissatisfaction with the many books with titles hke Foundations of Statistics. These books provide a needed description of the subject with examples of various statistical methods; but they do not satisfy the discerning reader because they do not explain why certain conclusions may be drawn from certain data and they do not discuss how statistics, the subject, meshes with the scientific process. We naively set out to fill in these gaps, but the situation is not so simple. What is desired is a tool—the one true statistics—which can be applied to data with certainty to justify conclusions, but what is available, in fact, are various competing theories of statistics. The careful reader may correctly point out the relation of this manuscript to po- modem epistemology, a philosophy which emphasizes that all human knowing—in fields as diverse as religion and science—is culture dependent and that therefore "truth" is not absolute. Take, for example, the "truths" of Christianity and Islam— wars have been fought over their differences. In the field of statistics there are, for example, Bayesians and sampling theorists. Carson (2003) states, "Surely it is better, postmodems tell us, to encourage insights that flow from many different perspectives. . . " In statistics, postmodernism is manifest at two levels. First, the findings of statistical applications are not about the true state of nature but about models of experiments on nature. |
Inhalt
| 1 | |
Mathematics and Its Applications | 9 |
The Evolution of Natural Scientists and Their Theories | 18 |
Law and Learning 33333 | 33 |
Introduction to Probability | 41 |
The Fair Betting Utility Interpretation of Probability | 54 |
Attitudes Toward Chance | 61 |
A Framework for Statistical Evidence | 75 |
A Critique of Bayesian Inference | 84 |
The LongRun Consequence of Behavior | 97 |
The Nature of Statistical Evidence | 116 |
The Science of Statistics | 122 |
Deductive Logic | 133 |
References | 143 |
| 151 | |
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accepted applied argument assumption axiom system axiomatic Bayes Bayesian inference behavior Borel's called Chapter checked concept concerned conclusion conditional probability consider consistent context deduction degree of belief density depends discussion distribution economic Eisenhart elementary events elliptic geometry equally equilibrium price Euclidean geometry evidential meaning example exist experimental outcome explain fact fair betting false flip formal science formulation frequency probability function hence hypothesis testing individual induction interpretation of probability knowledge Laplacian likelihood function likelihood principle likelihood ratio logical possibilities mathematics measure natural science observed obtain p-value p(yo parameter performed prediction prior probability axioms problem propensity probability propositional calculus random variables reason recipe relative frequency sample scientific method scientists Section significance level significance tests statements statistical evidence statistical inference statistical theory summarize Theorem tickets true value truth table truth values valid