Modeling spatio-temporal data using a Bayesian probabilistic cellular automata framework
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Regularly gridded, or cellular, discrete-valued spatio-temporal data are common in many application areas. Such data can be considered from many perspectives, including deterministic or stochastic cellular automata, where local rules govern the transition probabilities that describe the evolution of the state of the cells 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. This dissertation considers new approaches to augment latent processes to improve model predictions. To start, a novel approach utilizing a dynamic neighborhood structure with a latent process linked to the spatial domain via the use of empirical orthogonal functions is developed. An alternative augmentation strategy is developed that considers techniques from machine learning. This approach considers traditional Bayesian modeling techniques in conjunction with an echo state network to further improve model predictions. In addition to the echo state augmentation, symbolic regression is used to learn the functional form of available covariates for improved model accuracy and exploration of high dimensional interactions. A novel model weighting strategy is used in this echo state network augmentation approach, and prediction probability uncertainties are fully captured.
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Ph. D.