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Binary spatio-temporal data are common in many application areas. Such datacan be considered from many perspectives, including via deterministic orstochastic cellular automata, where local rules govern the transitionprobabilities that describe the evolution of the 0 and 1 states across spaceand time. One implementation of a stochastic cellular automata for such data iswith a spatio-temporal generalized linear model (or mixed model), with thelocal rule covariates being included in the transformed mean response. However,in real world applications, we seldom have a complete understanding of thelocal rules and it is helpful to augment the transformed linear predictor witha latent spatio-temporal dynamic process. Here, we demonstrate for the firsttime that an echo state network (ESN) latent process can be used to enhance thelocal rule covariates. We implement this in a hierarchical Bayesian frameworkwith regularized horseshoe priors on the ESN output weight matrices, whichextends the ESN literature as well. Finally, we gain added expressiveness fromthe ESNs by considering an ensemble of ESN reservoirs, which we accommodatethrough model averaging. This is also new to the ESN literature. We demonstrateour methodology on a simulated process in which we assume we do not know all ofthe local CA rules, as well as a fire evolution data set, and data describingthe spread of raccoon rabies in Connecticut, USA.

Bayesian Ensemble Echo State Networks for Enhancing Binary Stochastic Cellular Automata