Bayesian Evaluation of Non-Admissible Conditioning: The Case of Fisher Test.

We first analyse the general problem of admissible conditioning and next consider the evaluation of the loss of information when a non-admissible conditioning is used as an approximation of the exact posterior distribution. Considering the case of Fisher test, we evaluate from a Bayesian point of view how much information is lost when the sampling process for a 2x2 contingency table is analysed conditionally on the two margins. The numerical results obtained through simulation indicate that for a specific range of parameters the loss of information increases with the sample size and decreases with the precision of the a priori distribution. Hence such an approximation is shown to be a non-asymptotic one.