A Bayesian, Multivariate, Functional Linear Model with Spatially Varying Coefficients

• Activity Number: 91
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 9:30 PM to 10:15 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Christopher Krut* and Montserrat Fuentes and Brian J. Reich
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Functional Data ; Tropical Cyclones ; Multivariate Regression ; Spatially Varying Coefficients ; Bayesian

Abstract

The following paper considers an analysis of hurricane trajectories and intensities. Viewing the change in latitude, longitude and wind- speed as functions of time, we propose a functional data model which synthesizes existing methodology to simultaneously allow for multivariate, longitudinally observed data with noisy functional covariates. Spatially varying coefficients are incorporated using a combination of tensor product basis expansions with spatially dependent prior distributions on the basis coefficients. The proposed procedure is fully Bayesian and inference is performed using MCMC. Derivatives of selected covariate functions are incorporated in the model. The resulting multivariate, hierarchical Bayesian model, with spatially varying coefficients provides a sufficiently flexible model with a reasonable computational load.