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A Method for Simultaneous Variable Selection and Outlier ...

A Method for Simultaneous Variable Selection and Outlier ...

A Method for Simultaneous Variable Selection and Outlier

A Method for Simultaneous Variable Selection and Outlier Identication in Linear Regression Computational Statistics and Data Analysis (1996),22, 251-270. Jennifer Hoeting Colorado State University Adrian E. Raftery David Madigan University ofWashington March 1, 1996 Abstract We suggest a method for simultaneous variable selection and outlier identication based on the computation of posterior model probabilities. This avoids the problem that the model you select depends upon the order in which variable selection and outlier identication are carried out. Our method can nd multiple outliers and appears to be successful in identifying masked outliers. We also address the problem of model uncertainty via Bayesian model averaging. For problems where the number of models is large, we suggest a Markov chain Monte Carlo approach to approximate the Bayesian model average over the space of all possible variables and outliers under consideration. Software for implementing this approach is described. In an example, we show that model averaging via simultaneous variable selection and outlier identication improves predictive performance and provides more accurate prediction intervals as compared with any single model that might reasonably be selected. Key Words: Bayesian model averaging; Markov chain Monte Carlo model composition; Masking; Model uncertainty; Posterior model probability. Jennifer Hoeting is Assistant Professor of Statistics at the Department of Statistics, Colorado State University, Fort Collins, CO 80523 (e-mail: jah@lamar.colostate.edu). Adrian E. Raftery is Professor of Statistics and Sociology and David Madigan is Assistant Professor of Statistics at the Department of Statistics, Box 354322, University ofWashington, Seattle, WA 98195. The research of Raftery and Hoeting was partially supported by ONR Contract N-00014-91-J-1074. Madigan's research was partially supported by NSF grant no. DMS 92111627. 1

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