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sppmix: Poisson point process modeling using normal mixture models

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Abstract

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.

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Acknowledgements

We are grateful to three reviewers for their constructive comments and suggestions, and an Associate Editor and the two Editors, Drs. Sakamoto and Symanzik.

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  1. Department of Statistics, University of Missouri-Columbia, 134G Middlebush Hall, Columbia, MO, 65211, USA

    Athanasios C. Micheas & Jiaxun Chen

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  1. Athanasios C. Micheas
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  2. Jiaxun Chen
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Correspondence to Athanasios C. Micheas.

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Micheas, A.C., Chen, J. sppmix: Poisson point process modeling using normal mixture models. Comput Stat 33, 1767–1798 (2018). https://doi.org/10.1007/s00180-018-0805-z

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