A Mixture of Gaussian and Student's T Errors for a Robust and Accurate Parameter Estimation

• Activity Number: 302 - Bayesian Modeling
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Hyungsuk Tak* and Justin A. Ellis and Sujit K Ghosh
• Companies: SAMSI and Jet Propulsion Laboratory and North Carolina State University
• Keywords: outliers ; heavy tail ; Gibbs sampling ; time series ; hierarchical model ; Gaussian process

Abstract

A Gaussian error assumption, i.e., an assumption that the data are observed up to Gaussian noises, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student's t-distribution helps reduce the bias, but it may not be the most efficient choice for a parameter estimation because the assumption is uniformly applied to most of the normally observed data. We propose a mixture error assumption that selectively converts Gaussian errors into Student's t errors only for the data whose latent outlier indicators have the value unity. This mixture error can be easily incorporated into any parametric models that are built on a Gaussian error assumption, leveraging the best of the Gaussian and Student's t errors; a parameter estimation becomes not only robust but also accurate. Using simulated hospital profiling data and astronomical time series of brightness data, we demonstrate the potential for the proposed mixture error assumption to estimate parameters accurately in the presence of outliers.