Adaptive Bayesian sum of trees model for covariate-dependent spectral analysis

Area of Science:

• Biostatistics
• Time Series Analysis
• Nonparametric Statistics

Background:

• Biomedical time series often exhibit complex dependencies between covariates and power spectra.
• Existing methods may struggle to capture these intricate relationships and interactions effectively.

Purpose of the Study:

• To introduce a flexible and adaptive nonparametric method for estimating associations between multiple covariates and power spectra.
• To model complex dependencies and interactions in biomedical time series data.

Main Methods:

• Utilizes a Bayesian sum of trees model for capturing covariate-power spectrum relationships.
• Employs Bayesian penalized linear splines for nonparametric estimation of local power spectra.
• Applies a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm with reversible-jump MCMC for tree fitting.
• Incorporates a sparsity-inducing Dirichlet hyperprior for high-dimensional covariates and variable selection.

Main Results:

• The method accurately recovers smooth and abrupt changes in power spectra across multiple covariates.
• Simulations demonstrate the ability to precisely capture complex relationships and interactions.
• Successfully applied to analyze age-related changes in stride interval power spectra during gait maturation.

Conclusions:

• The proposed Bayesian sum of trees method offers a powerful tool for analyzing complex associations in time series data.
• Provides robust estimation and variable selection, particularly in high-dimensional settings.
• Enables deeper insights into developmental processes like gait maturation through power spectrum analysis.