ROBUST BAYESIAN REGRESSION ANALYSIS USING RAMSAY-NOVICK DISTRIBUTED ERRORS WITH STUDENT-T PRIOR

Abstract

This paper investigates bayesian treatment of regression modellingwith Ramsay - Novick (RN) distribution speciÖcally developed for robustinferential procedures. It falls into the category of the so-called heavy-taileddistributions generally accepted as outlier resistant densities. RN is obtainedby coverting the usual form of a non-robust density to a robust likelihoodthrough the modiÖcation of its unbounded ináuence function. The resultingdistributional form is quite complicated which is the reason for itslimited applications in bayesian analyses of real problems. With the helpof innovative Markov Chain Monte Carlo (MCMC) methods and softwarescurrently available, here we Örst suggested a random number generatorfor RN distribution. Then, we developed a robust bayesian modellingwith RN distributed errors and Student-t prior. The prior with heavy-tailedproperties is here chosen to provide a built-in protection against themisspeciÖcation of conáicting expert knowledge (i.e. prior robustness).This is particularly useful to avoid accusations of too much sub jective biasin the prior speciÖcation. A simulation study conducted for performanceassessment and a real-data application on the famously known"stack loss" data demonstrated that robust bayesian estimates with RNlikelihood and heavy-tailed prior are robust against outliers in all directionsand inaccurately speciÖed priors.