Protecting Against Gross Errors : The Aid of Bayesian Methods

A statistical model is characterized by a family of probabilty distribution functions. All inferences are then conditional on the hypothesis formalised by this family. The statistician often needs to protect himself against the consequences of a gross error relative to the basic hypothesis : either a specification error for the functionnal form of ¨P (X|θ), or the treatment of outliers. It will be shown in this paper that the bayesian approach offers a natural framework for treating thid kind of problem. Different methods are represented: robdutness analysis considering the sensivity of the inference tho the model specificztion; and approximations to Bayesian solutions which are for large class of models and sometimes preferable to exact solutions valid only for a particular model