Some Recent Developments in Statistics for Spatial Point Patterns

Møller, Jesper; Waagepetersen, Rasmus

doi:10.1146/annurev-statistics-060116-054055

Cited by 34 publications

(21 citation statements)

References 122 publications

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“…It is not only the variety of influencing processes acting and the interaction at different spatial and temporal scales that makes the identification and interpretation of processes leading to a certain spatial structure very difficult [3,4], but also the fact that different drivers may create similar patterns and similar processes may create different patterns in different settings. This has spurred statistical research and the presentation and discussion of various spatial point processes [5][6][7][8]. Modelling of a spatial point process was recently used to identify factors driving spatial distribution of trees at stand scales [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Seed Dispersal, Microsites or Competition—What Drives Gap Regeneration in an Old-Growth Forest? An Application of Spatial Point Process Modelling

Gratzer

Waagepetersen

2018

Forests

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The spatial structure of trees is a template for forest dynamics and the outcome of a variety of processes in ecosystems. Identifying the contribution and magnitude of the different drivers is an age-old task in plant ecology. Recently, the modelling of a spatial point process was used to identify factors driving the spatial distribution of trees at stand scales. Processes driving the coexistence of trees, however, frequently unfold within gaps and questions on the role of resource heterogeneity within-gaps have become central issues in community ecology. We tested the applicability of a spatial point process modelling approach for quantifying the effects of seed dispersal, within gap light environment, microsite heterogeneity, and competition on the generation of within gap spatial structure of small tree seedlings in a temperate, old growth, mixed-species forest. By fitting a non-homogeneous Neyman-Scott point process model, we could disentangle the role of seed dispersal from niche partitioning for within gap tree establishment and did not detect seed densities as a factor explaining the clustering of small trees. We found only a very weak indication for partitioning of within gap light among the three species and detected a clear niche segregation of Picea abies (L.) Karst. on nurse logs. The other two dominating species, Abies alba Mill. and Fagus sylvatica L., did not show signs of within gap segregation.

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Section: Introductionmentioning

confidence: 99%

“…Statistically, the spatial pattern of plants is a realization of a spatial point process. Recent advances in spatial statistics allow for applications of non-homogenous point process models that model the probability of spatial events depending on a set of spatial covariates [5,7,8,38].…”

Section: Introductionmentioning

confidence: 99%

Seed Dispersal, Microsites or Competition—What Drives Gap Regeneration in an Old-Growth Forest? An Application of Spatial Point Process Modelling

Gratzer

Waagepetersen

2018

Forests

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“…As an aside, the Campbell-Mecke formula has also been used for parametric inference, which is sometimes referred to as Takacs-Fiksel estimation. For an overview and references to the literature, see Møller & Waagepetersen (2017). Next, we consider the continuity properties of T κ (• ; , W ) and its limits as the bandwidth approaches zero and infinity.…”

Section: A New Approach To Bandwidth Selectionmentioning

confidence: 99%

A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions

Cronie

Lieshout

2018

Biometrika

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We propose a new bandwidth selection method for kernel estimators of spatial point process intensity functions. The method is based on an optimality criterion motivated by the Campbell formula applied to the reciprocal intensity function. The new method is fully nonparametric, does not require knowledge of higher-order moments, and is not restricted to a specific class of point process. Our approach is computationally straightforward and does not require numerical approximation of integrals.

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“…Due to the computational obstacles (especially if n is large) related to the calculation of the likelihood function, computationally easier approaches for statistical inference based on functional summary statistics, including ρ(u; β) and g(u, v; ν), together with estimation equations (obtained e.g. by minimum contrast methods, composite likelihoods or Palm likelihoods) have been suggested, see the review in Møller and Waagepetersen (2017). We will concentrate on the first and second order composite likelihoods (Guan, 2006;Waagepetersen, 2007;Tanaka et al, 2008;Waagepetersen and Guan, 2009;Guan et al, 2015;Zhuang, 2015).…”

Section: Composite Likelihood Estimationmentioning

confidence: 99%

Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

et al. 2019

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For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is a Cox process driven by an underlying log Gaussian random field (log GRF). This allows the representation of point aggregation, point vacuum and intermediate situations, with more or less rapid transitions between these different states depending on the properties of GRF. Very often, the covariance function of the GRF is assumed to be stationary. In this article, we give two examples where the sizes (that is, the number of points) and the spatial extents of point clusters are allowed to vary in space. To tackle such features, we propose parametric and semiparametric models of non-stationary LGCPs where the non-stationarity is included in both the mean function and the covariance function of the GRF. Thus, in contrast to most other work on inhomogeneous LGCPs, second-order intensity-reweighted stationarity is not satisfied and the usual two step procedure for parameter estimation based on e.g. composite likelihood does not easily apply. Instead we propose a fast three step procedure based on composite likelihood. We apply our modelling and estimation framework to analyse datasets dealing with fish aggregation in a reservoir and with dispersal of biological particles.

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Some Recent Developments in Statistics for Spatial Point Patterns

Cited by 34 publications

References 122 publications

Seed Dispersal, Microsites or Competition—What Drives Gap Regeneration in an Old-Growth Forest? An Application of Spatial Point Process Modelling

Seed Dispersal, Microsites or Competition—What Drives Gap Regeneration in an Old-Growth Forest? An Application of Spatial Point Process Modelling

A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions

Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

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