Frequentist Comparison of the Bayesian Significance Test for Testing the Median of the Lognormal Distribution

by Juliet Gratia D'Cunha and K. Aruna Rao.

Abstract: his paper focuses on the three Bayesian significance tests namely Bayes factor test, credible region test, full Bayesian significance test (FBST) and the reintroduced Bayesian/Non-Bayesian Likelihood Evidence test, with reference to the problem of testing specified value of the median of the two parameter lognormal distribution. These tests are compared in terms of type 1 error rate and power. The simulation results indicate that credible interval does not maintain level of significance for small samples. There is no difference in the power of the tests for the alternatives to the left and right of the null hypothesis. The other important conclusion that emerges is that these tests are robust against the specification of the prior distribution. Bayes factor test has the advantage of computational simplicity compared to the other three tests. The critical values for the Bayes factor and the evidence measure would be helpful for the scientists for taking a decision. In absence of critical values, guideline has been suggested for the use of FBST.

Key Words: Bayesian Significance Test, Bayes Factor, Credible Region, Full Bayesian Significance Test, Likelihood Evidence Test, Power of the Test

Authors:
Juliet Gratia D'Cunha, gratiajuliet@gmail.com
K. Aruna Rao, arunaraomu@gmail.com

Editor: Abd-Elfattah, a_afattah@hotmail.com

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