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We introduce two procedures for testing which are based on pooling the posterior evidence for the null hypothesis provided by the full Bayesian significance test and the posterior probability for the null hypothesis. Although the proposed procedures can be used in more general situations, we focus attention in tests for precise null hypothesis. We prove that the proposed procedure based on the linear operator is a Bayes rule. We also verify that it does not lead to the Jeffreys-Lindley paradox.doi:10.1214/11-bjps183 fatcat:gedw5r6axrcdtf5chnc7db7s7u