Asymptotic Normality with Small Relative Errors of Posterior Probabilities of Half-Spaces
Some examples of half-spaces of interest in parameter spaces are, in a clinical trial of a treatment versus placebo, the half-spaces where the treatment is (a) helpful or (b) harmful. Thus one may not only want to test the hypothesis that the treatment (c) makes no difference, but to assign posterior probabilities to (a), (b) and (c), under conditions as unrestrictive as possible on the choice of prior probabilities [e.g., Dudley and Haughton (2001)]. More generally, we have in mind applications to model selections as in the BIC criterion of Schwarz (1978) and its extensions [Poskitt (1987); Haughton (1988)], specifically to one-sided models and multiple data sets [Dudley and Haughton (1997)].
Key words and phrasesBernstein–von Mises theorem gamma tail probabilities intermediate deviations Jeffreys prior Mills’ ratio
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