A Weighted Dirichlet Process Mixture Modeling for Functional Clustering

• Activity Number: 175 - Bayesian Theory, Foundations, and Nonparametrics
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Wenyu Gao* and Inyoung Kim
• Companies: Virginia Tech and Virginia Tech
• Keywords: Bayesian Methods; Dirichlet Process Mixture (DPM); Functional Clustering; Weighted Dirichlet Process Mixture (WDPM)

Abstract

In this paper, we propose a weight function for weighted Dirichlet process mixture model (WDPM) and develop a Bayesian functional clustering method via WDPM. The important part of the statistical model is to specify the distribution of the error term/ random component. Although Dirichlet Process Mixture (DPM) has such flexibility, it does not take into account the covariates' information on the prior of each observation. DPM assumes that the error term/random component of each observation follows the same prior distribution. Therefore, DPM is not flexible enough when the error distributions are a mixture of heterogeneous distributions. To overcome this limitation, we can use the weighted Dirichlet process mixture (WDPM). Our weighted function allows us to have a flexible statistical model and clustering because the error term/random component's distribution for each observation can be automatically built and defined as unique via a weighted Dirichlet process mixture model. Construction of our weight function and its properties are illustrated. The advantages of our weight function are demonstrated using both simulation studies and empirical results.