A Bayesian approach to fitting Gibbs processes with temporal random effects

King, R., Illian, J. B. , King, S. E., Nightingale, G. F. and Hendrichsen, D. K. (2012) A Bayesian approach to fitting Gibbs processes with temporal random effects. Journal of Agricultural, Biological, and Environmental Statistics, 17(4), pp. 601-622. (doi:10.1007/s13253-012-0111-0) (PMID:AGR:IND500)

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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.

Item Type:Articles
Additional Information:The authors also gratefully acknowledge the financial support of Research Councils UK for Illian.
Glasgow Author(s) Enlighten ID:Illian, Professor Janine
Authors: King, R., Illian, J. B., King, S. E., Nightingale, G. F., and Hendrichsen, D. K.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Journal of Agricultural, Biological, and Environmental Statistics
ISSN (Online):1537-2693
Published Online:14 September 2012

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