Josh is currently a postdoctoral fellow in the CASCADE research group at Lawrence Berkeley National Laboratory. Prior to his postdoc, he completed his Ph.D. at the University of Missouri Columbia with Drs. Christopher Wikle and Erin Schliep. His main area of research is spatio-temporal statistical modeling with an emphasis on environmental and atmospheric applications.
Talk: Data-driven dynamical modeling for spatio-temporal statistics
Abstract: Classically, spatio-temporal data can be modeled using a mixed-effect representation where the fixed-effect captures the mean behavior and the random-effect describes the residual structure in the data. One approach for modeling each component statistically is to use dynamical equations parameterized with differential equations for the fixed-effect and a structured, low-rank representation for the random-effect: this approach encodes physical processes into the statistical model while enabling scalability to the large data sets that are now commonplace. While some of the dynamical relationships may be known, for real-world data sets we rarely know the complete form of the governing differential equations. Additionally, the low-rank model for the structured residual is typically based on some fixed decomposition that is specified a-priori to model estimation. Here, I present a fully Bayesian data-driven approach for discovering the form of dynamical equations parameterized by differential equations with uncertainty quantification. I illustrate the method’s ability to recover the synthetic Burgers’ equation and apply the method to infer the temporal evolution of the vorticity of the streamfunction. I will also present a data-driven approach to estimate the structure of a low-rank model representation parameterized by singular value decomposition where the basis functions from the decomposition are modeled dependently and with uncertainty quantification. I highlight the efficacy of the proposed low-rank approach on synthetic examples and apply it to sea surface temperature data over the northern Pacific.