Title: A robustness evaluation of some Bayesian testing problems
Authors: Lukas Arnroth - Uppsala University (Sweden) [presenting]
M Rauf Ahmad - Uppsala University (Sweden)
Abstract: The aim is to evaluate certain Bayesian tests for robustness under general classes of distributions. Whereas there is an ample amount of literature on the study of robustness for tests constructed under Neyman-Pearson theory, there is a serious lack of such study for Bayesian testing theory. To prepare the grounds for a solid case, we begin with Bayesian univariate mean tests, which is parallel to the frequentist t-tests. We evaluate them for robustness under a wider class of distributions, keeping a reasonable basis for the priors. Preliminary results are promising. We then extend it to the multivariate testing problems using potential alternatives to multivariate normal distribution, such as the elliptical class. Comparisons with corresponding frequentist tests, on grounds as similar as possible, are discussed. Finally, we extend the study in other directions, e.g., linear models.