Covariate-Guided Bayesian Mixture of Spline Experts for the Analysis of Multivariate Time Series

• Activity Number: 111 - Application and Development of Statistical Methods for Spatio-Temporal Data
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Haoyi Fu* and Ori Rosen and Lu Tang and Alison Hipwell and Theodore Huppert and Kate Keenan and Robert T Krafty
• Companies: University of Pittsburgh and University of Texas at El Paso and University of Pittsburgh and University of Pittsburgh and University of Pittsburgh and University of Chicago and Emory University
• Keywords: Multivariate time series; Bayesian mixture model; Reversible Jump MCMC; Neuroimaging; functional near-infrared spectroscopy; Covariate-guided model

Abstract

Time series from different sources are usually heterogeneous with high variability. We consider a collection of individuals, each with a multi-dimensional time series and propose a group-based approach to cluster these time series via a Bayesian mixture of smoothing splines. Our approach assumes each time series is a mixture of multiple dynamic components with mixing weights that depend on time-independent covariates. The posterior distribution is based on an augmented likelihood with latent indicators, and a smoothing spline prior is placed on the mixture components. We formulate our approach in a fully Bayesian framework and sample from the posterior distribution via a reversible jump Markov chain Monte Carlo (RJMCMC) sampling scheme, where the number of mixture components and model parameters are assumed unknown. The performance of our approach is evaluated by simulation studies, and is illustrated through analyses of functional near-infrared spectroscopy (fNIRS) data generated in a study of infants’ reaction to different interactions with their mothers.