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Abstract:
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In this presentation, we outline the equivalency between a continuous-state Markov model and a Poisson point process and show how, in cases of spatially-structured data, using a Poisson point process provides many advantages over traditional methods. While the link between Markov models and Poisson processes is well-known, our application is novel. Treating a Markov model as a Poisson point process allows us to represent the data using a flexible non-parametric model and leverage the wealth of sophisticated techniques available in spatial statistics to estimate continuous transition surfaces. After discussing the theoretical justification for our model, we showcase its features using simple toy examples in one dimension. Following this, we conclude by applying a Poisson point process model to SportVu player tracking data provided by the National Basketball Association in order to produce distinct maps of player movement for each team in the NBA.
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