Bayesian sensitivity analysis in elliptical linear regression models

• Published in: Journal of statistical planning and inference Vol. 86; no. 1; pp. 175 - 199
• Main Authors: Arellano-Valle, R.B., Galea-Rojas, M., Zuazola, P.Iglesias
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 15.04.2000; New York,NY Elsevier Science; Amsterdam
• Subjects: Bayes risks; Elliptical distributions; Exact sciences and technology; Influence measures; J-distance; L1-distance; Linear inference, regression; Linear regression models; Mathematics; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; 62J05; Elliptical distributions; Bayes risks; Influence measures; J-distance; Linear regression models; 62F15; L 1-distance; Bayes estimation; Bayes risk; Influence measure; Linear regression; Linear regression model; Student distribution; Posterior distribution; Elliptic distribution
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(99)00166-4

Bayesian influence measures for linear regression models have been developed mostly for normal regression models with noninformative prior distributions for the unknown parameters. In this work we extend existing results in several directions. First, we review influence measures for the ordinary normal regression model under conjugate prior distributions in unified framework. Second, we consider elliptical regression models with noninformative prior distributions for the model parameters and investigate the influence of a given subset of observations on the posterior distributions of the location and scale parameters. We found that these influence measures are Bayesian versions of classical counterparts to identify outliers or influential observations. Finally, we show that departures from normality within the multivariate elliptical family of distributions only affect the posterior distribution of the scale parameter.