Title: General Robust Bayes Pseudo-Posterior: Exponential Convergence results with Applications,
Abstract: Although Bayesian inference is an immensely popular paradigm among a large
segment of scientists including statisticians, most of the applications
consider the objective priors and need critical investigations (Efron, 2013,
Science). And although it has several optimal properties, one major drawback of
Bayesian inference is the lack of robustness against data contamination and
model misspecification, which becomes pernicious in the use of objective
priors. This paper presents the general formulation of a Bayes pseudo-posterior
distribution yielding robust inference. Exponential convergence results related
to the new pseudo-posterior and the corresponding Bayes estimators are
established under the general parametric set-up and illustrations are provided
for the independent stationary models and the independent non-homogenous
models. For the first case, the discrete priors and the corresponding maximum
posterior estimators are discussed with additional details. We further apply
this new pseudo-posterior to propose robust versions of the Bayes predictive
density estimators and the expected Bayes estimator for the fixed-design
(normal) linear regression models; their properties are illustrated both
theoretically as well as empirically.