Robust local empirical Bayes correction for Bayesian modeling

Abstract

This paper investigates a robust empirical Bayes correction for Bayesian modeling. We show the application of the model on income distribution. Income shock includes temporal and permanent shocks. We aim to eliminate temporal shock and permanent shock using two-step local empirical correction method. Our results show that only 6.7% of the observed income shocks were permanent shock, and the posterior (permanent) mean weekly income was reduced from the observed income 415 pounds to 202 pounds for the United Kingdom using the Living Costs and Food Survey in 2021-2022. Keywords: Empirical Bayes correction; Outliers; Bayesian modeling