Open Access
Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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. https://doi.org/10.1214/19-BA1173

Information

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

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.15 • No. 4 • December 2020
Back to Top