Conditional adaptive Bayesian spectral analysis of replicated multivariate time series

This article introduces a flexible nonparametric approach for analyzing the association between covariates and power spectra of multivariate time series observed across multiple subjects, which we refer to as multivariate conditional adaptive Bayesian power spectrum analysis (MultiCABS). The proposed procedure adaptively collects time series with similar covariate values into an unknown number of groups and nonparametrically estimates group-specific power spectra through penalized splines. A fully Bayesian framework is developed in which the number of groups and the covariate partition defining the groups are random and fit using Markov chain Monte Carlo techniques. MultiCABS offers accurate estimation and inference on power spectra of multivariate time series with both smooth and abrupt dynamics across covariate by averaging over the distribution of covariate partitions. Performance of the proposed method compared with existing methods is evaluated in simulation studies. The proposed methodology is used to analyze the association between fear of falling and power spectra of center-of-pressure trajectories of postural control while standing in people with Parkinson's disease.