A weighted strategy to handle likelihood uncertainty in Bayesian inference

The sensitivity of posterior inferences to model specification can be considered as an indicator of the presence of outliers, that are to be considered as highly unlikely values under the assumed model. The occurrence of anomalous values can seriously alter the shape of the likelihood function and lead to posterior distributions far from those one would obtain without these data inadequacies. In order to deal with these hindrances, a robust approach is discussed, which allows us to obtain outliers’ resistant posterior distributions with properties similar to those of a proper posterior distribution. The methodology is based on the replacement of the genuine likelihood by a weighted likelihood function in the Bayes’ formula.