Space and circular time log Gaussian Cox processes with application to crime event data

Alan Gelfand, Duke University

Friday, April 20, 2018 - 3:30pm

We view the locations and times of a collection of crime events as a space-time point pattern modeled as either a nonhomogeneous Poisson process or a more general log Gaussian Cox process. We need to specify a space-time intensity. Viewing time as circular, necessitates valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular time. Additionally, crimes are classified by crime type and each crime event is marked by day of the year which we convert to day of the week.

We present marked point pattern models to accommodate such data. Our specifications take the form of hierarchical models which we fit within a Bayesian framework. We consider model comparison between the nonhomogeneous Poisson process and the log Gaussian Cox process as well as separable vs. nonseparable covariance specifications. Our motivating dataset is a collection of crime events for the city of San Francisco during the year 2012.

We conclude briefly with some new work in progress which seeks to assess the “velocity” of crime as an illustration of the velocity of a point pattern over space and time. Here, we extend some earlier work on the velocity of climate change; we now seek the instantaneous rate of change in risk for a crime event in a given direction in units of distance per time.

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