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Unified Conditional Frequentist and Bayesian Testing of Composite Hypotheses
Author(s) -
DASS SARAT C.,
BERGER JAMES O.
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00326
Subject(s) - frequentist inference , bayes factor , mathematics , bayesian probability , frequentist probability , econometrics , statistics , posterior probability , statistical hypothesis testing , prior probability , conditional probability distribution , bayesian inference
Testing of a composite null hypothesis versus a composite alternative is considered when both have a related invariance structure. The goal is to develop conditional frequentist tests that allow the reporting of data‐dependent error probabilities, error probabilities that have a strict frequentist interpretation and that reflect the actual amount of evidence in the data. The resulting tests are also seen to be Bayesian tests, in the strong sense that the reported frequentist error probabilities are also the posterior probabilities of the hypotheses under default choices of the prior distribution. The new procedures are illustrated in a variety of applications to model selection and multivariate hypothesis testing.