Local robustness and influence for contamination classes of prior distributions

Abstract

In the well-known ε-contamination class of prior distributions Γ = {τr(0) : τr(0) = (1 -ε)π o (Θ) + εq(θ), q G Q) ,ε represents the degree of uncertainty on the base prior τro(0) and Q the allowed class of contaminations.We argue here that the uncertainty we have on τr o (0) typically is stronger on its tails than on its body.This idea is formalized through a more general ε(0)-contamination class that might be seen as a local robustiflcation of πo(θ).When Q is defined by quantile constraints, the admissible classes of functions ε(θ) capable of maintaining the prior information for the resulting priors π(θ) are characterized and robust posterior analysis is carried out.Influence analysis is also considered.In this setting Frechet derivatives are useful tools: they are easily interpreted and easily computed.Interactive robustness based on influence analysis is discussed.