Covariate Dependent Spectral Analysis of Multivariate Time Series with Application to Heart Rate Variability During Sleep

• Activity Number: 486
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Ori Rosen *+ and Robert Krafty and David Stoffer and Daniel Buysse and Martica Hall
• Companies: University of Texas at El Paso and Temple University and University of Pittsburgh and University of Pittsburgh and University of Pittsburgh
• Keywords: Heart Rate Variability ; Multivariate Time Series ; Smoothing Splines ; Spectral Analysis ; Whittle Likelihood

Abstract

We introduce a novel approach to assessing the association between covariates and multivariate power spectra. A Bayesian tensor product smoothing spline ANOVA model for covariate dependent multivariate power spectral analysis is developed that nonparametrically accounts for covariate effects while preserving the positive definite and Hermitian structures of spectral matrices. MCMC techniques based on the Whittle likelihood are used to fit the model and allow for automated nonparametric inference on the association between covariates and power spectra as well as nonlinear functions of power spectra, such as coherence. The proposed approach is motivated by a study of sleep in older adults and used to assess the connections between self-reported measures of sleep and autonomic system activity via the spectral analysis of heart rate variability across different periods of sleep.