Open Conference Systems, STATISTICS AND DATA SCIENCE: NEW CHALLENGES, NEW GENERATIONS

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Space and circular time log Gaussian Cox processes with application to crime event data
Alan E. Gelfand, Shinichiro Shirota

Last modified: 2017-05-20

Abstract


We view the locations and times of a collection of crime events as a space-time pointpattern modeled as either a nonhomogeneous Poisson process or a more general log GaussianCox process. We need to specify a space-time intensity. Viewing time as circular, necessitatesa valid separable and nonseparable covariance functions over a bounded spatial region crossedwith circular time. Additionally, crimes are classified by crime type and each crime event ismarked by day of the year which we convert to day of the week.We present marked point pattern models to accommodate such data. Our specificationstake the form of hierarchical models which we fit within a Bayesian framework. We considermodel comparison between the nonhomogeneous Poisson process and the log Gaussian Coxprocess as well as separable vs. nonseparable covariance specifications. Our motivatingdataset is a collection of crime events for the city of San Francisco during the year 2012.