Simple Outlier Detection with Dirichlet Process Mixtures

• Activity Number: 567
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew Shotwell*+ and Elizabeth H. Slate
• Companies: Vanderbilt University School of Medicine and Medical University of South Carolina
• Keywords: outlier ; product partition model ; Dirichlet process mixture ; Bayes factor ; MAP estimate ; optimization

Abstract

We introduce a Bayesian inference mechanism for outlier detection using the product partition model equivalent of a Dirichlet process mixture. Outliers are detected by forming a maximum a posteriori (MAP) estimate of the data partition. Observations that comprise small or singleton clusters in the estimated partition are considered outliers. We present a novel interpretation of the Dirichlet process precision parameter and demonstrate its utility in outlier detection problems. The precision parameter is used to form an outlier detection criterion based on the Bayes factor for a partition with outliers versus a class of partitions with fewer or no outliers. We also introduce a computational method for MAP estimation that is free of posterior sampling and guaranteed to find a MAP estimator in finite time. Our computational method is compared with several established methods in a real data example. Implementation of the methodology for product partitions of linear models is available in the R package profdpm.