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Abstract:
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Many natural phenomena can be described as points on the plane, for example, longitude-latitude of tornados, forest fires and earthquakes. We refer to these collections of points as point patterns and the points as the events. In this paper we develop and study statistical models in order to describe stochastically these point patterns, as well as, capture their evolution over time. Often, some additional information (a mark) is available that further describes the event. Such models are known as marked space-time point processes (MSTPPs) and the points are referred to as the events of the process. When the events are assumed to interact with each other then we appeal to Markov MSTPPs (MMSTPPs) in order to model such behavior. In particular, we employ a hierarchical Bayesian framework in order to model point patterns, their underlying process models (that help realize the points), as well as, the parameters of the data and process models. We illustrate how to perform forecasting and consider the inclusion of relevant covariate information for a general class of pair-wise interaction MMSTPPs. The models are illustrated with applications to atmospheric science data.
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