On robustness of the relative belief ratio and the strength of its evidence with respect to the geometric contamination prior

The relative belief ratio becomes a widespread tool in many hypothesis testing problems. It measures the statistical evidence that a given statement is true based on a combination of data, model and prior. Additionally, a measure of the strength is used to calibrate its value. In this paper, robustness of the relative belief ratio and its strength to the choice of the prior is studied. Specifically, the Gâteaux derivative is used to measure their sensitivity when the geometric contaminated prior is used. Examples are presented to illustrate the results.