Modeling the growth of objects through a stochastic process of random sets

Dey, Rima; Micheas, Athanasios C.

doi:10.1016/j.jspi.2014.03.007

Cited by 3 publications

(2 citation statements)

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“…Now in order to build an evolution model for ∆(t k ), we consider the model proposed by Dey and Micheas (2014); that is, we decompose ∆(t k ) using the special LDU decomposition method originally proposed by Dunson et al (2003) and further developed by Chen et al ( 2011) as follows…”

Section: Stage 2: Process Stagementioning

confidence: 99%

“…Novel marked Poisson space-time point process models are developed via conditioning arguments that allow for a natural interpretation of the different components of the intensity function, be it the location, the mark, or the time component. Moreover, novel dynamic Markov marked space-time point process models are developed, thus, extending the Gibbs point process models that where first considered as process models in the random set models of Micheas and Wikle (2009), and Dey and Micheas (2014).…”

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confidence: 99%

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Dynamic spatial-temporal point process models via conditioning

Okenye¹

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We propose and investigate dynamic spatial-temporal point process models for independent and interacting events. The models for independent events are dynamic spatial-temporal Poisson point process (DSTPPP) model that account for temporal and spatial clustering. The models proposed for events with interaction are Markov (Gibbs) space-time point process models. We model the intensity function of a DSTPPP via conditioning arguments that allow for additional interpretations and inclusion of well-known point process models as special cases. Depending on the nature of the questions to be answered, the in- tensity function of a DSTPPP can be modeled in several ways. First, we develop models via conditioning on the time component of the events and then consider conditioning on the location component of the events. Modeling, simulation and computation are accomplished in a fully hierarchical Bayesian framework. Finally, we focus on dynamic marked Markov space-time point processes, where the events are allowed to interact with each other across time and space. Once again the hierarchical Bayesian framework is invaluable in this case, since it allows us to introduce dynamic process models via conditioning. The methodolo- gies are illustrated using simulated data, and several applications, including modeling and inference for earthquake events in California, and tornado events in Missouri.

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Section: Stage 2: Process Stagementioning

confidence: 99%

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confidence: 99%