On Parameter Estimation for Pairwise Interaction Point Processes

Diggle, Peter J.; Fiksel, Thomas; Grabarnik, Pavel; Ogata, Yosihiko; Stoyan, Dietrich; Tanemura, Masaharu

doi:10.2307/1403548

Cited by 85 publications

(78 citation statements)

References 26 publications

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“…Note that the model exhibits interactions between pairs of points only. Pairwise interaction models appear to be a useful and flexible class of models for regular patterns, but probably not so for clustered patterns (Diggle et al 1994;Gates and Westcott 1986;and M01ler 1999).…”

Section: Haggstrom Mnm Van Lieshout and J Mollermentioning

confidence: 99%

Characterization Results and Markov Chain Monte Carlo Algorithms Including Exact Simulation for Some Spatial Point Processes

Häggström

Lieshout²,

Møller³

1999

Bernoulli

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The area-interaction process and the continuum random-cluster model are characterized in terms of certain functional forms of their respective conditional intensities. In certain cases, these two point process models can be derived from a bivariate point process model which in many respects is simpler to analyse and simulate. Using this correspondence we devise a two-component Gibbs sampler, which can be used for fast and exact simulation by extending the recent ideas of Propp and Wilson. We further introduce a Swendsen -Wang type algorithm. The relevance of the results within spatial statistics as well as statistical physics is discussed.

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Section: Haggstrom Mnm Van Lieshout and J Mollermentioning

confidence: 99%

Characterization Results and Markov Chain Monte Carlo Algorithms Including Exact Simulation for Some Spatial Point Processes

Häggström

Lieshout²,

Møller³

1999

Bernoulli

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show abstract

“…Values of γ between 0 and 1 discourage but do not forbid events to be within distance ρ of each other. Note that the normalizing constant, C, of the Strauss process can be difficult to calculate, especially for processes demonstrating strong inhibition (see Diggle et al 1994). …”

Section: Minefield Processmentioning

confidence: 99%

Classification of Mixtures of Spatial Point Processes via Partial Bayes Factors

Walsh¹,

Raftery²

2003

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Motivated by the problem of minefield detection, we investigate the problem of classifying mixtures of spatial point processes. In particular we are interested in testing the hypothesis that a given dataset was generated by a Poisson process versus a mixture of a Poisson process and a hard-core Strauss process. We propose testing this hypothesis by comparing the evidence for each model by using partial Bayes factors. We use the term partial Bayes factor to describe a Bayes factor, a ratio of integrated likelihoods, based on only part of the available information, namely that information contained in a small number of functionals of the data. We applied our method to both real and simulated data, and considering the difficulty of classifying these point patterns by eye, our approach overall produced good results.

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“…4, with the solid line on the left being the estimate of and the solid line on the right being the estimate of V. CONCLUSION Although the sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is easy to compute, the evaluation of its performance is a challenging problem. The limit theorem of Appendix A shows that in the case of sparseness, the distribution of could be approximated by the distribution of the shot-noise random variable , and it is then shown that the distribution of could be computed using (6) or (12), depending on the form of the interaction function. While the analysis of (6) in Section IV-A is straightforward, the derivation of (12) in Section IV-B is more complicated, and the details are found in Appendix B. Extensions are treated in Appendix C. Finally, we note that our analysis of the sparseness conditions in Appendix D in the case of square regions leads to a simply computable value for the constant which appears in the characteristic function of in (5 (3) and (4)) and Now, the hypotheses of our theorem are sufficient for us to apply [3 …”

Section: Remarkmentioning

confidence: 99%

Performance analysis of hypothesis testing for sparse pairwise interaction point processes

Gubner

Chang

Hayat

2000

IEEE Trans. Inform. Theory

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Abstract-The sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is well-known; however, the evaluation of its performance is a very difficult problem. In this paper it is shown that the distribution of the sufficient statistic can be approximated by the distribution of a Poisson-driven shot-noise random variable, which can be readily computed.Index Terms-Gibbs point process, pairwise interaction point process, Poisson approximation, shot noise.

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On Parameter Estimation for Pairwise Interaction Point Processes

Cited by 85 publications

References 26 publications

Characterization Results and Markov Chain Monte Carlo Algorithms Including Exact Simulation for Some Spatial Point Processes

Characterization Results and Markov Chain Monte Carlo Algorithms Including Exact Simulation for Some Spatial Point Processes

Classification of Mixtures of Spatial Point Processes via Partial Bayes Factors

Performance analysis of hypothesis testing for sparse pairwise interaction point processes

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