Sparsity in nonlinear dynamic spatiotemporal models using implied advection

Calculating posterior means and variances of the state vectors in dynamic spatiotemporal models can be computationally burdensome. The challenge of calculating the posterior parameters while avoiding inverting any dense matrices is addressed. Nearest neighbor Gaussian processes and a number of dynamic modeling tricks will be used. To employ these techniques in both linear and nonlinear settings, a nontraditional discretization of an advection-diffusion stochastic partial differential equation is presented. The combination of these methods allows a nonlinear dynamic spatiotemporal model to be fit quickly. The methods are employed in a simulation comparing the proposed model and a reduced-rank model in terms of model fits and run times and then by analyzing a data set of Pacific sea surface temperature.