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BAYESIAN TESTS FOR SOME PRECISE HYPOTHESES ON MULTI‐NORMAL MEANS
Author(s) -
Groenewald P.C.N.,
Waal D.J.
Publication year - 1989
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1989.tb00984.x
Subject(s) - bayes factor , prior probability , mathematics , null hypothesis , conjugate prior , bayesian probability , alternative hypothesis , statistics , statistical hypothesis testing , normal distribution , posterior probability , bayes' theorem , p value , econometrics
Summary Bayesian counterparts of some standard tests concerning the means of multi‐normal distribution are discussed. In particular the hypothesis that the multi‐normal mean is equal to a specified value, and the hypothesis that the means are equal. Lower bounds on the Bayes factor in favour of the null hypothesis are obtained over the class of conjugate priors. The P‐value, or observed significance level of the standard sampling‐theoretic test procedure are compared with the posterior probability. The results correspond closely with those of Good (1967), Berger & Sellke (1987), Pepple (1988) and others and illustrate the conflict between posterior probabilities and P ‐values as measures of evidence.