  Many studies of biomedical time series signals aim to measure the association
between frequency-domain properties of time series and clinical and behavioral
covariates. However, the time-varying dynamics of these associations are
largely ignored due to a lack of methods that can assess the changing nature of
the relationship through time. This article introduces a method for the
simultaneous and automatic analysis of the association between the time-varying
power spectrum and covariates. The procedure adaptively partitions the grid of
time and covariate values into an unknown number of approximately stationary
blocks and nonparametrically estimates local spectra within blocks through
penalized splines. The approach is formulated in a fully Bayesian framework, in
which the number and locations of partition points are random, and fit using
reversible jump Markov chain Monte Carlo techniques. Estimation and inference
averaged over the distribution of partitions allows for the accurate analysis
of spectra with both smooth and abrupt changes. The proposed methodology is
used to analyze the association between the time-varying spectrum of heart rate
variability and self-reported sleep quality in a study of older adults serving
as the primary caregiver for their ill spouse.
