A Bayesian Spatial Change-Point Model for Functional Clustering

• Activity Number: 348
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Zhen Zhang*+ and Sarat C Dass and Chae Young Lim and Tapabrata Maiti
• Companies: Michigan State University and Michigan State University and Michigan State University and Michigan State University
• Keywords: Change point analysis ; Dirichlet process priors ; Clustering ; Spatial random efffects ; Bayesian nonparametrics ; Conditional Auto-regressive

Abstract

We propose a Bayesian model to detect change points for the temporal data such as evolution of cancer mortality rates, and to capture the spatial correlations between sites and clustering pattern of sites that exhibit similar trends. Our methodology performs simultaneous detecting and clustering on the space of functions, and takes into account the spatial dependence using conditional auto-regressive model. The Bayesian analysis is carried out by eliciting a Dirichlet process prior on the functional space and using improper default prior. The resulting posterior distribution, however, is shown to be valid and proper. The Gibbs updating procedures are also proposed and validated. Simulation studies were conducted to evaluate the methodology, and further investigate the sensitivity to prior specification and the performance of competing models that are with spatial, non-spatial random effect, and without random effect. Through the analysis of real data, the proposed model can nicely characterize local data features including change points, the rate of changes, and clusters of sites that exhibited similar trends.