Testing of hypothesis using the bayes factor

Abstract

In any testing problem, the most popular procedure to draw a conclusion regarding the null and alternative hypotheses is to use the p-value of the test. If the p-value is below a certain level of significance “the test is rejected” and if not “we fail to reject the null hypothesis based on the observed data”. What if we wanted to know how much more favoured the alternative hypothesis was, based on the data observed, than the null hypothesis. The p-value only taking into account the distribution under the null setup fails to answer this question. This is primarily why we use the Bayes Factor. The purpose of this paper is to provide a brief overview of the Bayes Factor. Using two simple examples the use of Bayes Factor in testing problems is depicted and conclusions drawn. The paper tries to establish the Bayes Factor as another practical tool for testing of hypotheses.