Hierarchical Bayesian Random Sets with Applications to Growth Models

• Activity Number: 406
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Athanasios Micheas*+
• Companies: University of Missouri at Columbia
• Keywords: Random Object ; Finite Mixture Models ; Hierarchical Bayesian Model ; Growth Models ; Data Augmentation ; Reversible Jump MCMC

Abstract

We propose and study a novel Bayesian Hierarchical framework to model objects stochastically as well as capture the growth or evolution of an object, based on random sets. We efficiently model a random set via a multistage hierarchical Bayesian framework, and using finite mixture models of possibly varying dimension. Such models require the use of data augmentation techniques as well as Reversible Jump MCMC sampling methods. Several growth models are proposed, including Hereditary, Birth-Death and Mixed type, as well as the corresponding Bayesian formulation that provides inference and prediction. The models are exemplified through some simulations.