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Abstract:
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We address the problem of how to achieve robust inference in a Bayesian setting. To do so, we decompose a model into two parts, the Head and the Tail. The Head of the model incorporates informed prior knowledge and may have a parametric form. It will often define the primary characteristics about which inference is to be made. The Tail incorporates vaguer information. It accommodates model misfit, whether this be systematic departures of modest size from the Head, or individual or small pockets of cases that are difficult to describe (outliers). We advocate use of a carefully tailored nonparametric Bayesian component for the Tail, because such a component is flexible and has full support. Head and Tail modeling applies to many statistical problems such as classification, clustering, regression, etc. We compare results to those from parametric and nonparametric Bayesian models.
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