Adaptive Bayesian Sum of Trees Model for Covariate Dependent Spectral Analysis

Oregon Convention Center 

This talk introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated using Bayesian penalized linear splines. The trees are random and fit using a Bayesian backfitting Markov chain Monte Carlo algorithm that sequentially considers tree modifications via reversible-jump techniques. For high-dimensional covariates, a sparsity-inducing Dirichlet hyperprior is considered, which provides sparse estimation of covariate effects and efficient variable selection. Empirical performance is evaluated via simulations to demonstrate the method's ability to accurately recover complex relationships and interactions. The methodology is used to study gait maturation in young children by evaluating age-related changes in power spectra of stride interval time series in the presence of other covariates.