Conditional adaptive Bayesian spectral analysis of replicated multivariate time series

Li, Zeda; Bruce, Scott A.; Wutzke, Clinton J.; Yang, Long

doi:10.1002/sim.8884

Cited by 4 publications

(5 citation statements)

References 41 publications

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“…This model decomposes the modified Cholesky decomposition defined in (7) as a bivariate function into products of univariate functions of ν and ω. Parameters a are coefficients for functions that are products of linear functions of both ν and ω, b are coefficients for functions that are products of linear functions of ω and nonlinear functions of ν, c are coefficients for functions that are products of nonlinear functions of ω and linear functions of ν, and d are coefficients for functions that are products of nonlinear functions of ω and ν. In principle, other Bayesian approaches, such as those in [6,33], can be adapted to estimate the conditional copula spectral matrix. These adaptive Bayesian methods partition the covariate space into an unknown but finite number of groups in which the number and location of covariate partition points are random and adaptively estimated using reversible-jump Markov chain Monte Carlo (RJMCMC) techniques.…”

Section: Bayesian Tensor Product Spline Modelmentioning

confidence: 99%

“…However, they are designed for analysis of a single time series and are unable to quantify the associations between the replicated time series and covariates. On the other hand, methods for spectral analysis of replicated time series have also recently been proposed, which include semi-parametric functional mixed-effects models [28,8], nonparametric methods [14], and adaptive Bayesian approaches [6,29,7,33]. However, these methods have roots in the classical autocovariancebased spectral density, and thus are subject to the known limitations of the classical second-order spectral analysis.…”

Section: Introductionmentioning

confidence: 99%

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Robust conditional spectral analysis of replicated time series

2023

Statistics and Its Interface

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Classical second-order spectral analysis, which is based on the Fourier transform of the autocovariance functions, focuses on summarizing the oscillatory behaviors of a time series. However, this type of analysis is subject to two major limitations: first, being covariance-based, it cannot captures oscillatory information beyond the second moment, such as time-irreversibility and kurtosis, and cannot accommodate heavy-tail dependence and infinite variance; second, focusing on a single time series, it is unable to quantify the association between multiple time series and other covariates of interests. In this article, we propose a novel nonparametric approach to the spectral analysis of multiple time series and the associated covariates. The procedure is based on the copula spectral density kernel, which inherits the robustness properties of quantile regression and does not require any distributional assumptions such as the existence of finite moments. Copula spectral density kernels of different pairs are modeled jointly as a matrix to allow flexible smoothing. Through a tensor-product spline model of Cholesky components of the conditional copula spectral density matrix, the approach provides flexible nonparametric estimates of the copula spectral density matrix as nonparametric functions of frequency and covariate while preserving geometric constraints. Empirical performance is evaluated in simulation studies and illustrated through an analysis of stride interval time series.

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Section: Bayesian Tensor Product Spline Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust conditional spectral analysis of replicated time series

2023

Statistics and Its Interface

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“…Bruce et al (2018) proposed an adaptive Bayesian method that can capture both smooth and abrupt changes in power spectra across a covariate. Li et al (2021) adapted the method of Bruce et al (2018) for covariate-dependent spectral analysis of replicated multivariate time series. However, these methods are not readily extendable to incorporate multiple covariates, which hinders their applicability to many important studies.…”

Section: Introductionmentioning

confidence: 99%

“…Li et al. (2021) adapted the method of Bruce et al. (2018) for covariate‐dependent spectral analysis of replicated multivariate time series.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Bayesian Sum of Trees Model for Covariate-Dependent Spectral Analysis

Wang

Bruce

2022

Biometrics

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This paper 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.

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“…Bruce et al (2018) proposes an adaptive Bayesian method that can capture both smooth and abrupt changes in power spectra across a covariate. Li et al (2021) adapts the method of Bruce et al (2018) for covariate-dependent spectral analysis of replicated multivariate time series. However, these methods are not readily extendable to incorporate multiple covariates, which hinders their applicability to many important studies.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Bayesian Sum of Trees Model for Covariate Dependent Spectral Analysis

Wang¹,

Li²,

Bruce³

2021

Preprint

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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.

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Conditional adaptive Bayesian spectral analysis of replicated multivariate time series

Cited by 4 publications

References 41 publications

Robust conditional spectral analysis of replicated time series

Robust conditional spectral analysis of replicated time series

Adaptive Bayesian Sum of Trees Model for Covariate-Dependent Spectral Analysis

Adaptive Bayesian Sum of Trees Model for Covariate Dependent Spectral Analysis

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