On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox

Authors

  • Benito Vittorio Frosini Università Cattolica del Sacro Cuore, Milano

DOI:

https://doi.org/10.6092/issn.1973-2201/38

Abstract

Two topics, connected with Neyman-Pearson theory of testing hypotheses, are treated in this article. The first topic is related to the information content of an experiment; after a short outline of ordinal comparability of experiments, the two most popular informa-tion measures – by Fisher and by Kullback-Leibler – are considered. As far as we require a comparison of two experiments at a time, the superiority of the couple (a,b) of the two error probabilities in the Neyman-Pearson approach is easily established, owing to their clear operational meaning. The second topic deals with the so called Jeffreys – or Lindley – paradox: it can be shown that, if we attach a positive probability to a point null hypothesis, some «paradoxical» posterior probabilities – in a Bayesian approach – result in sharp contrast with the error probabilities in the Neyman-Pearson approach. It is argued that such results are simply the outcomes of absurd assumptions, and it is shown that sensible assumptions about interval – not point – hypotheses can yield posterior probabilities perfectly compatible with the Neyman-Pearson approach (although one must be very careful in making such comparisons, as the two approaches are radically different both in assumptions and in purposes).

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How to Cite

Frosini, B. V. (2007). On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox. Statistica, 64(2), 271–286. https://doi.org/10.6092/issn.1973-2201/38

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