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.

翻译：二元时空数据在许多应用领域普遍存在。此类数据可从多种视角分析，包括确定性或随机元胞自动机，其中局部规则支配着描述0和1状态在时空上演化的转移概率。针对此类数据的一种随机元胞自动机实现采用时空广义线性模型（或混合模型），将局部规则协变量纳入变换后的均值响应中。然而在现实应用中，我们鲜少能完全理解局部规则，因此通过潜在时空动态过程增强变换线性预测器十分有益。本文首次证明了回声状态网络（ESN）潜在过程可用于增强局部规则协变量。我们在分层贝叶斯框架中实现该方法，对ESN输出权重矩阵采用正则化马蹄形先验，这同时扩展了ESN文献研究。最后，通过考虑ESN储备池集成模型（采用模型平均方法处理）获得更强表达能力，这亦属ESN文献中的创新。我们在假设未知全部元胞自动机局部规则的模拟过程上、火势演化数据集上以及描述美国康涅狄格州浣熊狂犬病传播的数据上验证了该方法的有效性。