Robust Bayesian Regression using a Finite Partition Approximation to the Residual Density

• Activity Number: 106
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences*
• Author(s): David Dunson*+
• Affiliation(s): National Institute of Environmental Health Sciences
• Keywords: Bayesian ; Moment Constraints ; Nonlinear Regression ; MCMC algorithm ; Integrated Likelihood

Abstract

Consider the semiparametric model Y = f(X; beta) + sigma R, where f is a known function, beta are unknown regression parameters, sigma is the unknown residual variance, and R ~ G is a standardized residual having E(R)=0 and V(R) = 1, with G unknown. This article considers a new approach for Bayesian inference on (beta,sigma) with G considered a nuisance. A method is proposed for nonparametrc modeling of G on a finite partition B_1(g),...,B_K(g) of R^1, which is defined by using percentiles of a known distribution G_0 to form a set of intervals that is then centered to constrain E(R) ~ 0 and V(R) ~ 1. We propose to eliminate the nuisance parameters g from the likelihood by: (i) replacing g with it's MAP estimate conditional on (beta, sigma); or (ii) integrating out g. In both cases, Markov chain Monte Carlo is used for posterior computation. The approach is illustrated with bioassay data.