Fitting Nonlinear Latent Diffusion Process to Irregularly Spaced Longitudinal Data with Efficient MCMC Algorithm

• Activity Number: 250
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Zhaohua Lu*+ and Sy-Miin Chow and Andrew Sherwood and Hongtu Zhu
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and Duke University and The University of North Carolina at Chapel Hill
• Keywords: Nonlinear diffusion processes ; Irregularly spaced longitudinal data ; Bayesian methods ; Markov chain Monte Carlo ; Multiresolution algorithms ; Latent variables

Abstract

Irregularly spaced longitudinal data have become increasingly prevalent in various fields. However, approaches to handle dynamic models for irregularly spaced data are comparatively lacking, especially for data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear latent differential equation models with subject-specific effects to irregularly spaced data. A Bayesian approach with a modified Brownian Bridge sampler and an efficient multiresolution algorithm is proposed and its performance is evaluated through the Lorenz equations and double-well potential model. An application to a set of 24-hour ambulatory cardiovascular data is used to illustrate the practical utility of the proposed approach.