The discrepancy of P-values and posterior probability: Two-sided hypothesis of variance of normal distribution with unknown mean

ABSTRACT

This article is concerned with the comparison of P-value and Bayesian measure in point null hypothesis for the variance of Normal distribution with unknown mean. First, using fixed prior for test parameter, the posterior probability is obtained and compared with the P-value when an appropriate prior is used for the mean parameter. In the second, lower bounds of the posterior probability of H₀ under a reasonable class of prior are compared with the P-value. It has been shown that even in the presence of nuisance parameters, these two approaches can lead to different results in the statistical inference.

KEYWORDS:

• Lower bound of posterior probability
• nuisance parameter
• P-value
• sensitivity.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62F03