A Bayesian robustness measure in significance tests for equivalence tests

In this article, the local sensitivity of non linear prior quantities in Bayesian significance tests with respect to the choice of a prior distribution is considered. We propose sensitivity indices using the Gâteaux derivative to evaluate the rate of change of statistical functionals defined over the space of prior probability measures. These sensitivity indices are easy to interpret and calculate. We apply the proposed methodology to equivalence tests for two independent binomial proportions to quantify the local sensitivity of quantities in significance tests, such as adaptive significance level and power, with respect to the choice of the prior distribution. We present an application in sensory analysis and consumer research to illustrate the proposed methodology.