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Although Bayesian inference is an immensely popular paradigm among a largesegment of scientists including statisticians, most applications considerobjective priors and need critical investigations (Efron, 2013, Science). Whileit has several optimal properties, a major drawback of Bayesian inference isthe lack of robustness against data contamination and model misspecification,which becomes pernicious in the use of objective priors. This paper presentsthe general formulation of a Bayes pseudo-posterior distribution yieldingrobust inference. Exponential convergence results related to the newpseudo-posterior and the corresponding Bayes estimators are established underthe general parametric set-up and illustrations are provided for theindependent stationary as well as non-homogeneous models. Several additionaldetails and properties of the procedure are described, including the estimationunder fixed-design regression models.

General Robust Bayes Pseudo-Posterior: Exponential Convergence results with Applications