sppmix: Poisson point process modeling using normal mixture models. (English) Zbl 1417.62009

Micheas, Athanasios C.; Chen, Jiaxun

Comput. Stat. 33, No. 4, 1767-1798 (2018).

Summary: This paper describes the package sppmix for the statistical environment R. The sppmix package implements classes and methods for modeling spatial point patterns using inhomogeneous Poisson point processes, where the intensity surface is assumed to be a multiple of 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. In addition, several approaches have been implemented in order to handle the standard label switching issue which arises in any modeling approach involving mixture models. We adapt a hierarchical Bayesian framework in order to model the intensity surfaces and have implemented two major algorithms in order to estimate the parameters of the mixture models involved: the data augmentation and the birth-death Markov chain Monte Carlo (DAMCMC and BDMCMC). We used C++ (via the Rcpp package) in order to implement the most computationally intensive algorithms.

MSC:

62-04	Software, source code, etc. for problems pertaining to statistics
62M30	Inference from spatial processes
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
62F15	Bayesian inference
65C40	Numerical analysis or methods applied to Markov chains

Keywords:

birth-death MCMC; data-augmentation MCMC; hierarchical Bayesian models; marked point process via conditioning; Poisson point process

Software:

RcppArmadillo; sppmix; lgcp; fields; Rcpp; R-Geo; ggplot2; INLA; R; spatstat

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