ABSTRACT
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.
ACKNOWLEDGMENTS
We are very grateful to the Editor and two anonymous referees for their helpful comments and valuable suggestions on a previous version of the paper. This research has been sponsored by DGES (Spain) under grant PB-98-0797.