Modeling Spatial Poisson and Related Point Processes

Implements classes and methods for modeling spatial point patterns using inhomogeneous Poisson point processes, where the intensity surface is assumed to be analogous to a finite additive mixture of normal components and the number of components is a finite, fixed or random integer. Extensions to the marked inhomogeneous Poisson point processes case are also presented. We provide an extensive suite of R functions that can be used to simulate, visualize and model point patterns, estimate the parameters of the models, assess convergence of the algorithms and perform model selection and checking in the proposed modeling context.

Mixture models for spatial point patterns

The sppmix package implements classes and methods for modeling spatial point process data using Poisson point processes where the intensity surface is assumed to be a multiple of a finite additive mixture of normal components.

We utilize the ppp and owin classes from the spatstat package in order to describe a point pattern. We further introduce a normmix class for handling 2d mixtures of bivariate normal components, and help us build the Poisson point process intensity surface.

Data augmentation MCMC (DAMCMC) and Birth-Death MCMC (BDMCMC) are the two main methods we have implemented for estimating the Poisson intensity surface, in a Bayesian framework.

The MCMC algorithms are implemented in C++ using Rcpp and RcppArmadillo, and were optimized after extensive testing, meaning that this approach is significantly faster than some other implementations of mixture models.

Plotting is accomplished using the rgl package in order to create 3d plots of the intensity surfaces. In addition, the fields and ggplot packages were used for 2d plots.

To learn more about sppmix, start with the basic tutorials at http://www.stat.missouri.edu/~amicheas/sppmix/sppmix_tutorial_links.html