On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox
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 information measures – by Fisher and by Kul...
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| Format: | Article |
| Language: | English |
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University of Bologna
2007-10-01
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| Series: | Statistica |
| Online Access: | http://rivista-statistica.unibo.it/article/view/38 |
| _version_ | 1811192430759772160 |
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| author | Benito Vittorio Frosini |
| author_facet | Benito Vittorio Frosini |
| author_sort | Benito Vittorio Frosini |
| collection | DOAJ |
| description | 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 information 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). |
| first_indexed | 2024-04-11T23:52:38Z |
| format | Article |
| id | doaj.art-1491f6620aa84ca6b3ee344ef94fac1b |
| institution | Directory Open Access Journal |
| issn | 0390-590X 1973-2201 |
| language | English |
| last_indexed | 2024-04-11T23:52:38Z |
| publishDate | 2007-10-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Statistica |
| spelling | doaj.art-1491f6620aa84ca6b3ee344ef94fac1b2022-12-22T03:56:26ZengUniversity of BolognaStatistica0390-590X1973-22012007-10-0164227128610.6092/issn.1973-2201/3834On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy ParadoxBenito Vittorio Frosini0Università Cattolica del Sacro Cuore, MilanoTwo 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 information 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).http://rivista-statistica.unibo.it/article/view/38 |
| spellingShingle | Benito Vittorio Frosini On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox Statistica |
| title | On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox |
| title_full | On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox |
| title_fullStr | On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox |
| title_full_unstemmed | On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox |
| title_short | On Neyman-Pearson Theory: Information Content of an Experiment and a Fancy Paradox |
| title_sort | on neyman pearson theory information content of an experiment and a fancy paradox |
| url | http://rivista-statistica.unibo.it/article/view/38 |
| work_keys_str_mv | AT benitovittoriofrosini onneymanpearsontheoryinformationcontentofanexperimentandafancyparadox |