Adaptive Bayesian Sum of Trees Model for Covariate Dependent Spectral Analysis
This provides a flexible method for analyzing covariate-dependent spectral patterns in biomedical time series, though it is incremental as it builds on existing Bayesian tree and spline techniques.
The authors tackled the problem of estimating how multiple covariates affect the power spectra of time series, particularly in biomedical contexts, by introducing a Bayesian sum of trees model that captures complex dependencies and interactions, with simulations showing accurate recovery of relationships and application to gait maturation in children revealing age-related spectral changes.
This article 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 nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers tree modifications via reversible-jump MCMC techniques. For high-dimensional covariates, a sparsity-inducing Dirichlet hyperprior on tree splitting proportions is considered, which provides sparse estimation of covariate effects and efficient variable selection. By averaging over the posterior distribution of trees, the proposed method can recover both smooth and abrupt changes in the power spectrum across multiple covariates. Empirical performance is evaluated via simulations to demonstrate the proposed method's ability to accurately recover complex relationships and interactions. The proposed 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.