STATISTICAL INFERENCE AND APPLICATIONS OF A SPATIAL-TEMPORAL MARKOV RANDOM FIELD

<p dir="ltr">Markov random fields (MRF) form a broad class of stochastic models frequently applied to spatial data. A generalization of Markov chains, the MRF models capture spatial correlation by introducing dependence among data on the surface through a chosen neighborhood structure. We introduce a three-dimensional MRF with such neighborhoods that incorporate spatial patterns as well as the time dimension to create a spatio-temporal model. The proposed clique configuration forces spatial dependencies to evolve through time, reflecting dynamics of an observed process. Our statistical inference approach to the Markov Random field is likelihood based. The complex form of the joint distribution of observed spatially and longitudinally dependent data does not allow a closed form of the likelihood function. We show that the pseudolikelihood of this MRF model, as applied to Bernoulli data, can be conveniently expressed as logistic regression. The theory of maximum pseudolikelihood estimation shows that our resulting parameter estimates are consistent and asymptotically normal. As a case study, we use our Markov random field specification to model the dynamics and spread of wildfires. We show that the model can be used to detect wildfire spread and explain the direction and speed at which a wildfire is moving, as well as changes in their behavior in time and in space. We also apply the Markov random field as a generative model in simulations to develop accurate, timely, and probabilistic wildfire spread forecasts, to complement state-of-the-art physical models.</p>