Random set models for growth with applications to nowcasting
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] We develop models to capture the growth or evolution of objects over time as well as provide forecasts to describe the object in future states utilizing information from the current state. For this purpose, we propose methodologies to model random sets (RS) using Germ-Grain theory. The RS that describes the objects in a hierarchical Bayesian framework can have either overlapping or non-overlapping grains. We investigate three types of growth models, namely, hereditary, birth-death and mixed type. In the hereditary growth model, the germ of a grain arises from the previous state, whereas in birth-death it does not belong to any of the previous grains. The mixed type is a combination of the other two. Furthermore, we consider two approaches to capture the growth process with the first developing a bound on the individual grain of the RS and the second evolving the parameters defining the grains directly. Estimation of model parameters is carried out using Markov chain Monte Carlo (MCMC). In addition, we develop an alternative approach to Reversible Jump MCMC or Birth-Death MCMC that is capable of sampling a varying dimensional parameter space. This method is based on the Boolean model, the most commonly used RS. We illustrate our methodologies on simulated data in order to demonstrate its ability of fitting the underlying growth process and forecasting an unobserved state. The methodologies are further exemplified with several applications to nowcasting of severe weather precipitation fields as obtained from weather radar images, where severe storm cells are treated as random sets.
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