Hybrids of Gibbs Point Process Models and Their Implementation

Baddeley, Adrian; Turner, Rolf; Mateu, Jorge; Bevan, Andrew

doi:10.18637/jss.v055.i11

Cited by 51 publications

(44 citation statements)

References 56 publications

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“…Several other forms of g ijk can be used, and multiple forms can be combined as described in Baddeley et al . (). We shall not pursue them here as either (a)they can be approximated by the Strauss or saturation model as the interaction functions

β_{ij}^{normalT} {boldg}_{ij}

are step functions over spatial scales, (b)there is not sufficient data available to estimate very fine details over many spatial scales or (c)they are computationally costly (e.g.…”

Section: The Gibbs Model and Gibbs Model Fitting With Variable Selectionmentioning

confidence: 99%

Detecting Multivariate Interactions in Spatial Point Patterns with Gibbs Models and Variable Selection

Rajala

Murrell

Olhede

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology thus develops high dimensional data understanding in the point process setting. The method is based on modelling the patterns by using a flexible Gibbs point process model to characterize point‐to‐point interactions at different spatial scales directly. By using the Gibbs framework significant interactions can also be captured at small scales. Subsequently, the Gibbs point process is fitted by using a pseudolikelihood approximation, and we select significant interactions automatically by using the group lasso penalty with this likelihood approximation. Thus we estimate the multivariate interactions stably even in this setting. We demonstrate the feasibility of the method with a simulation study and show its power by applying it to a large and complex rainforest plant population data set of 83 species.

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β_{ij}^{normalT} {boldg}_{ij}

are step functions over spatial scales, (b)there is not sufficient data available to estimate very fine details over many spatial scales or (c)they are computationally costly (e.g.…”

Section: The Gibbs Model and Gibbs Model Fitting With Variable Selectionmentioning

confidence: 99%

Detecting Multivariate Interactions in Spatial Point Patterns with Gibbs Models and Variable Selection

Rajala

Murrell

Olhede

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…9). We analyzed the residual of the fitted models using the K-residual function used in Baddeley et al (2013). The K-residual from the first model showed a positive association between the points, as it lies outside the confidence intervals at a range from 10 to 20 m. The second model added to the previous hard-core process is a Geyer process (see Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Hybrids are particularly useful for modeling interactions at multiple scales. This method has been demonstrated to be useful on a real dataset on human social interaction (Baddeley et al 2013).…”

Section: Spatial Analysis and Statistical Modelingmentioning

confidence: 99%

“…Spatial point processes (e.g., Gibbs models) exhibit spatial interactions at only a single spatial scale, whereas natural processes exhibit dependence at multiple scales (Delicado et al 2010). Thus, with the use of spatial statistics, like new hybrid spatial point processes (Baddeley et al 2013), we are able to show the joint effects of biotic processes and abiotic heterogeneity on the spatial pattern of the halophyte community.…”

Section: Introductionmentioning

confidence: 99%

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A spatial pattern analysis of the halophytic species distribution in an arid coastal environment

Badreldin

Mateu

Youssef³

et al. 2015

Environ Monit Assess

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Registro de acceso restringido Este recurso no está disponible en acceso abierto por política de la editorial. No obstante, se puede acceder al texto completo desde la Universitat Jaume I o si el usuario cuenta con suscripción. Registre d'accés restringit Aquest recurs no està disponible en accés obert per política de l'editorial. No obstant això, es pot accedir al text complet des de la Universitat Jaume I o si l'usuari compta amb subscripció. Restricted access item This item isn't open access because of publisher's policy. The full--text version is only available from Jaume I University or if the user has a running suscription to the publisher's contents.

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“…The spatstat R-package (Baddeley and Turner (2005); Baddeley et al (2013)) supports the model fitting of spatial point processes, in particular Poisson processes, and related inference and diagnostic tools. The function ppm fits a spatial point process to an observed point pattern and allows the inclusion of covariates.…”

Section: Covariate Selectionmentioning

confidence: 99%

Analyzing car thefts and recoveries with connections to modeling origin–destination point patterns

2020

Self Cite

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For a given region, we have a dataset composed of car theft locations along with a linked dataset of recovery locations which, due to partial recovery, is a relatively small subset of the set of theft locations. For an investigator seeking to understand the behavior of car thefts and recoveries in the region, several questions are addressed. Viewing the set of theft locations as a point pattern, can we propose useful models to explain the pattern? What types of predictive models can be built to learn about recovery location given theft location? Can the dependence between theft locations and recovery locations be formalized? Can the flow between theft sites and recovery sites be captured?Origin-destination modeling offers a natural framework for such problems. However, here the data is not for areal units but rather is a pair of point patterns, with the recovery point pattern only partially observed. We offer modeling approaches for investigating the questions above and apply the approaches to two datasets. One is small from the state of Neza in Mexico with areal covariate information regarding population features and crime type. A second, much larger one, is from Belo Horizonte in Brazil but lacks covariates.

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Hybrids of Gibbs Point Process Models and Their Implementation

Cited by 51 publications

References 56 publications

Detecting Multivariate Interactions in Spatial Point Patterns with Gibbs Models and Variable Selection

Detecting Multivariate Interactions in Spatial Point Patterns with Gibbs Models and Variable Selection

A spatial pattern analysis of the halophytic species distribution in an arid coastal environment

Analyzing car thefts and recoveries with connections to modeling origin–destination point patterns

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