A SUITABLE BAYESIAN APPROACH IN TESTING POINT NULL HYPOTHESIS: SOME EXAMPLES REVISITED
Miguel Angel Gómez-Villegas, Paloma Maı́n, Luis Angel Rioja Sanz · Communication in Statistics- Theory and Methods · 2002
In the problem of testing the point null hypothesis versus , with a previously given prior density for the parameter θ, we propose the following methodology: to fix an interval of radius ϵ around θ0 and assign a prior mass, π0, to H 0 computed by the density πθ over the interval , spreading the remainder, , over H 1 according to π (θ). It is shown that for Lindley';s paradox, the Normal model with some different priors and Darwin–Fisher';s example, this procedure makes the posterior probability of H 0 and the p-value matching better than if the prior mass assigned to H 0 is 0.5.