Abstract: We study robust Bayesian prediction problems using the posterior regret Г-minimax (PRGM) approach. We provide a unified theory for PRGM prediction under a very general class of regret loss functions that includes the squared error, linear-exponential, entropy and many other loss functions as special cases. We apply our results to the problem of predicting unknown parameters for finite populations under different superpopulation models (normal and non-normal, with or without auxiliary variables) and several classes of prior distributions, including the commonly used ϵ-contaminated class of priors. Our results are augmented with real-world applications and simulation studies.

Key words and phrases: Bayes predictor, finite population, posterior regret Г-minimax, robust Bayesian analysis.