On ε-contaminated priors with quantile and piece-wise unimodality constraints

Abstract

In this work we examine the e-contamination model of prior densities γ={π:π=(1-ε)π₀(θ)+εq: qεG}, where π₀(θ) is the base elicited prior, q is a contamination belonging to some suitable class G and ε reflects the amount of error in π₀(θ). Various classes with shape and/or quantile constraints are analysed, and a posterior robust analysis is carried out. It turns out that quantile restrictions alone do not produce asymptotical rational behaviour, so it is unavoidable to introduce shape constraints as well. The conclusions are in line with those of O'Hagan and Berger (1988). Illustrations related to testing hypothesis and likelihood sets are given.

Keywords:

• classes of ε-contaminated priors
• imprecision
• robust Bayes
• shape and quant He constraints