Bayesian Outlier Detection with Dirichlet Process Mixtures

We introduce a Bayesian inference mechanism for outlier detection using the augmented 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 offer 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 an outlier partition versus a class of partitions with fewer or no outliers. We further introduce a computational method for MAP estimation that is free of posterior sampling, and guaranteed to find a MAP estimate in finite time. The novel methods are compared with several established strategies in a yeast microarray time series.