Comparison Between Bayesian Lower Bound and P-value
نویسنده (گان)
چکیده مقاله
For deciding a hypothesis, in significant test p-value and in Bayesian test Bayes factor or posterior probability of null hypothesis is used. It is well known that, in univariate case the posterior probability of null hypothesis is typically much larger than the p-value. It has been shown that the difference is depend on sample size, type of hypothesis, and prior distribution that was chosen. In multivariate case, the difference is also depend on dimension of the parameter, which is to be tested. Dependence of significance testing and Bayesian testing on sample size and specified prior distribution is criticized by some Bayesian researches. They suggested to compare p-value with lower bound of posterior probability of null hypothesis on a class of prior distribution. This paper reviews the problem of testing a point null hypothesis. Of interest is the relationship between p-value and Baysisan measures of evidence against the null hypothesis. The lower bound of the posterior of null hypothesis over three classes of prior distribution are derived and compared with the p-value.

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