A Bayesian approach to fitting Gibbs processes with temporal random effects

Ruth King, Janine Baerbel Illian, Stuart Edward King, Glenna Faith Nightingale, Ditte Hendrichsen

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
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We consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a “snapshot” of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis.
Original languageEnglish
Pages (from-to)601-622
Number of pages22
JournalJournal of Agricultural, Biological and Environmental Statistics
Issue number4
Early online date14 Sept 2012
Publication statusPublished - Dec 2012


  • Data augmentation
  • Markov chainMonte Carlo
  • Mixed effects model
  • Muskoxen data
  • Spatial and temporal point processes


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