A Bayesian Multivariate Functional Dynamic Linear Model
Seminar | January 25 | 4-5 p.m. | 1011 Evans Hall
Daniel Kowal, Cornell University
I will present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. I will illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent Brexit referendum, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis.