Open Access
December 2020 Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices
Shiwei Lan, Andrew Holbrook, Gabriel A. Elias, Norbert J. Fortin, Hernando Ombao, Babak Shahbaba
Bayesian Anal. 15(4): 1199-1228 (December 2020). DOI: 10.1214/19-BA1173


Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive Δ -Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat’s local field potential activity in a complex sequence memory task.


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Shiwei Lan. Andrew Holbrook. Gabriel A. Elias. Norbert J. Fortin. Hernando Ombao. Babak Shahbaba. "Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices." Bayesian Anal. 15 (4) 1199 - 1228, December 2020.


Published: December 2020
First available in Project Euclid: 4 November 2019

Digital Object Identifier: 10.1214/19-BA1173

Keywords: dynamic covariance modeling , geometric methods , posterior contraction , spatio-temporal models , Δ-Spherical Hamiltonian Monte Carlo

Vol.15 • No. 4 • December 2020
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