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Title: Adaptive Bayesian covariate dependent spectral analysis of multiple time series Authors:  Yakun Wang - George Mason University (United States) [presenting]
Zeda Li - City University of New York (United States)
Scott Bruce - George Mason University (United States)
Abstract: A flexible and adaptive method is proposed for estimating the association between multiple covariates and the power spectrum 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. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The tree structures in this model are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers modifications to trees via reversible jump MCMC techniques. By averaging over the posterior distribution of tree structures to estimate the covariate-dependent power spectrum, the proposed method can recover both smooth and abrupt changes in the power spectrum across covariates. Empirical performance is evaluated via simulations, which demonstrates the proposed method's ability to accurately recover complex nonlinear associations and interaction effects on the power spectrum.