Modeling gibbs point processes through basic function decompositions

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] We consider non-homogeneous pairwise interaction point process models, where the global and local effect functions are modeled using basis function expansions. For data with interaction between points, we use an ordered exponential prior on the interaction coefficients. For data without interaction we use independent normal priors. The basis coefficients are estimated in a Bayesian framework where we use the double Metropolis-Hastings algorithm. The corresponding hyperparameters can be drawn using a Gibbs sampler. The proposed methodology is exemplified through simulation and through locations of waterstriders and locations of forest fires from the waterstriders dataset and the clmfires dataset, respectively, both from the spatstat R package (Baddeley et al., 2015). The model is then extended to allow for the inclusion of covariates. The methodology is illustrated using the location of kidnappings in a selected area in the southern region of Chicago for 2015, where we include as covariate information the American Community Survey 5-year period estimate of median income at the Census tract level.