Comparison between Frequentist Test and Bayesian Test to Variance Normal in the Presence of Nuisance Parameter: One-sided and Two-sided Hypothesis

This article is concerned with the comparison P-value and Bayesian measure for the variance of Normal distribution with mean as nuisance paramete. Firstly, the P-value of null hypothesis is compared with the posterior probability when we used a fixed prior distribution and the sample size increases. In second stage the P-value is compared with the lower bound of posterior probability when the prior distribution is belonged to a class of reasonable distributions. It was shown that even for fixed sample size the P-value is less than the lower bound. This is not the case for one-sided hypothesis. There is a reconcilability between these two criterion.