Carlos Alberto de Bragança Pereira^* and Julio Michael Stern

Instituto de Matemática e Estatística, Universidade de São Paulo, 05315-970, Brasil
E-mail: [email protected]; [email protected]
^* Author to whom correspondence should be addressed

Received: 9 February 1999 / Accepted: 9 April 1999 / Published: 27 October 1999

Abstract: A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the "Highest Posterior Density Region" that is "tangent" to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the "tangent" region.

Keywords: Bayes factor; numerical integration; global optimization; p-value; posterior density.