Spectral Inverted-Wishart: A Flexible Cross-Covariance Function for Multivariate Spatio-Temporal Data

• Activity Number: 707
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Leo Duan* and Rhonda Szczesniak and Xia Wang
• Companies: Duke University and Cincinnati Children's Hospital and University of Cincinnati
• Keywords: Covariance convolution ; High dimensional cross-covariance ; Inverted-Wishart ; Marginal Gaussian ; Spatial regression

Abstract

We introduce a new class of cross-covariance function, spectral inverted-Wishart, to address the challenges of multivariate modeling in high dimensional spatial data. We construct the cross-covariance with a spectrally convoluted inverted-Wishart distribution. This function not only ensures that every spatial outcome has its own set of smooth parameters, but is also very flexible in capturing any weak or negative inter-variate correlation. The cross-covariance matrix is guaranteed to be positive definite and suitable for the marginal Gaussian assumption. Utilizing the Bayesian paradigm, we provide a very efficient algorithm that is linearly scalable to the size of the data. We demonstrate the potentials of our approach, with a spatio-temporal regression on the temperature and precipitation data in North America, produced by 3 Weather Research and Forecasting systems.