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

Shinichiro Shirota, Alan E. Gelfand

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


We view the locations and times of a collection of crime events as a space–time point pattern. Then, with either a nonhomogeneous Poisson process or with a more general Cox process, we need to specify a space–time intensity. For the latter, we need a random intensity which we model as a realization of a spatio-temporal log Gaussian process. Importantly, we view time as circular not linear, necessitating valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular time. In addition, crimes are classified by crime type. Furthermore, each crime event is recorded by day of the year, which we convert to day of the week marks. The contribution here is to develop models to accommodate such data. Our specifications take the form of hierarchical models which we fit within a Bayesian framework. In this regard, we consider model comparison between the nonhomogeneous Poisson process and the log Gaussian Cox process. We also compare 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 have location, hour, day of the year, and crime type for each event. We investigate models to enhance our understanding of the set of incidences.

Original languageEnglish
Pages (from-to)481-503
Number of pages23
JournalAnnals of Applied Statistics
Issue number2
Publication statusPublished - Jun 2017


  • Derived covariates
  • Hierarchical model
  • Marked point pattern
  • Markov chain Monte Carlo
  • Separable and nonseparable covariance functions
  • Wrapped circular variables

Fingerprint Dive into the research topics of 'Space and circular time log Gaussian Cox processes with application to crime event data'. Together they form a unique fingerprint.

Cite this