Fundamental problems in fitting spatial cluster process models

Baddeley, Adrian; Davies, Tilman M.; Hazelton, Martin L.; Rakshit, S.; Turner, Rolf

doi:10.1016/j.spasta.2022.100709

Cited by 7 publications

(1 citation statement)

References 52 publications

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“…This might result in biased (and unreliable) estimates. We refer to Baddeley et al (2022) for a detailed classification of causes for these practical difficulties.…”

Section: Minimum Contrast For First-order Intensity Estimationmentioning

confidence: 99%

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

D’Angelo¹,

Adelfio²

2023

Preprint

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In this paper, we exploit a result in point process theory, knowing the expected value of the K-function weighted by the true first-order intensity function. This theoretical result can serve as an estimation method for obtaining the parameters estimates of a specific model, assumed for the data. The motivation is to generally avoid dealing with the complex likelihoods of some complex point processes models and their maximization. This can be more evident when considering the local second-order characteristics, since the proposed method can estimate the vector of the local parameters, one for each point of the analysed point pattern. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes.

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“…This might result in biased (and unreliable) estimates. We refer to Baddeley et al (2022) for a detailed classification of causes for these practical difficulties.…”

Section: Minimum Contrast For First-order Intensity Estimationmentioning

confidence: 99%

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

D’Angelo¹,

Adelfio²

2023

Preprint

View full text Add to dashboard Cite

show abstract

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

D’Angelo,

Adelfio

2024

Stat Papers

View full text Add to dashboard Cite

In this paper, we harness a result in point process theory, specifically the expectation of the weighted K-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

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A New Construction of Covariance Functions for Gaussian Random Fields

Wu,

Micheas

2024

Sankhya A

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Fundamental problems in fitting spatial cluster process models

Cited by 7 publications

References 52 publications

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

A New Construction of Covariance Functions for Gaussian Random Fields

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