On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox
AbstractTwo 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).
How to Cite
Frosini, B. V. (2004). 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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