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