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Activity Number: 509 - New Approaches to Modeling and Inference for Complex Space-Time Data
Type: Topic Contributed
Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract #329792 Presentation
Title: Flexible Dynamic Modeling of Correlation and Covariance Matrices for Spatio-Temporal Data Analysis
Author(s): Babak Shahbaba* and Andrew James Holbrook and Gabriel Elias and Norbert J. Fortin and Hernando Ombao and Shiweil Lan
Companies: UCI and UC Irvine and UC Irvine and UC Irvine and UC Irvine and CalTech
Keywords: Dynamic covariance modeling; Spatio-temporal models; Geometric methods; Hamiltonian Monte Carlo

Modeling correlation (and covariance) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. Here, we propose a novel Bayesian framework based on modeling the correlation matrix as a product of vectors on unit spheres. The covariance matrix is then modeled by using its decomposition into correlation and variance matrices. This approach allows us to induce flexible prior distributions for covariance matrices by proposing a wide range of distributions on spheres (e.g. the squared-Dirichlet distribution). Additionally, our method can be easily extended to dynamic settings in order to model real-life spatio-temporal processes with complex dependence structures (e.g., brain signals during cognitive tasks). To handle the intractability of the resulting posterior, we introduce a novel sampling algorithm called Adaptive Spherical Hamiltonian Monte Carlo. Using an example of Normal-Inverse-Wishart problem, a simulated periodic process, and an analysis of local field potential data, we demonstrate the validity and effectiveness of our proposed framework for (dynamic) modeling of covariance and correlation matrices.

Authors who are presenting talks have a * after their name.

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