Statistical Evidence: A Likelihood Paradigm

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CRC Press, Jun 1, 1997 - Mathematics - 191 pages
Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.
 

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This thoughtful book continues an important tradition of statistical reasoning that challenges the usual machinery of hypothesis tests and p-values. It is well worth reading if you are interested in the foundations of inference, but it would be tough going without a good elementary course in statistics. --DHK 

Contents

The first principle
1
NeymanPearson theory
35
Fisherian theory
61
Paradigms for statistics
83
Resolving the paradoxes from the old paradigms
109
Looking at likelihoods
123
Nuisance parameters
151
Bayesian statistical inference
167
The paradox of the ravens
177
Index
189
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