The Bayes/Non-Bayes Compromise and the Multinomial Distribution

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Abstract
Compromises between Bayesian and non-Bayesian significance testing are exemplified by examining distributions of criteria for multinominal equiprobability. They include Pearson's X2, the likelihood-ratio, the Bayes factor F, and a statistic G that previously arose from a Bayesian model by “Type II Maximum Likelihood.” Its asymptotic distribution, implied by the theory of the “Type II Likelihood Ratio,” is remarkably accurate into the extreme tail. F too can be treated as a non-Bayesian criterion and is almost equivalent to G. The relationship between F and its own tail area sheds further light on the relationship between Bayesian and “Fisherian” significance.

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