  Although Bayesian inference is an immensely popular paradigm among a large
segment of scientists including statisticians, most applications consider
objective priors and need critical investigations (Efron, 2013, Science). While
it has several optimal properties, a 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 as well as non-homogeneous models. Several additional
details and properties of the procedure are described, including the estimation
under fixed-design regression models.
