Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices

Shiwei Lan, Andrew Holbrook, Gabriel A. Elias, Norbert J. Fortin, Hernando Ombao, Babak Shahbaba

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1199-1228
Number of pages30
JournalBayesian Analysis
Volume15
Issue number4
DOIs
StatePublished - 2020

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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