Stochastic Volatility Regression for Functional Data Dynamics

• Activity Number: 326
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Bin Zhu*+ and David Dunson
• Companies: Duke University and Duke University
• Keywords: Functional data dynamics ; Gaussian process ; Nonparametric regression ; State space model ; Stochastic volatility regression

Abstract

This article proposes a stochastic hierarchical model to investigate the relationship between the covariates of interest and the volatility of functional data dynamics in a multi-subject setting. The derivatives of the mean functions of trajectories are modeled by Gaussian processes through stochastic differential equations, where the instantaneous volatilities depend on covariates. Hence, we allow for estimating the fluctuation of the functional data and assessing its association with the covariates. A Markov chain Monte Carlo algorithm is used for posterior computation, coupled with Euler approximation and data augmentation if derivatives of the mean functions have no explicit transition density. The methods are used to allow volatility in blood pressure trajectories during pregnancy to vary across women and with covariates.