TY - JOUR
AU - Frosini, Benito Vittorio
PY - 2004/01/01
Y2 - 2021/10/17
TI - On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox
JF - Statistica
JA - Stat
VL - 64
IS - 2
SE - Articles
DO - 10.6092/issn.1973-2201/38
UR - https://rivista-statistica.unibo.it/article/view/38
SP - 271-286
AB - 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).
ER -