Statistical Analysis and Modelling of Spatial Point Patterns

Illian, Janine B.; Penttinen, Antti; Stoyan, Helga; Stoyan, Dietrich

doi:10.1002/9780470725160

Cited by 1,148 publications

(2,295 citation statements)

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“…The goal of the search would be to optimize (separately or in combination) various figures of merit that quantify the likelihood that this group is a family, such as difference between average color of family members and average color of background objects. Spatial point processes, a general statistical term for cluster algorithms, could also be effectively employed to determine figures of merit (e.g., Illian et al 2008). For example, these could be used to identify regions of proper element space that contained significant overabundances compared to a model of the background.…”

Section: Resultsmentioning

confidence: 99%

Identifying Collisional Families in the Kuiper Belt

Marcus

Ragozzine

Murray-Clay

et al. 2011

ApJ

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The identification and characterization of numerous collisional families-clusters of bodies with a common collisional origin-in the asteroid belt has added greatly to the understanding of asteroid belt formation and evolution. More recent study has also led to an appreciation of physical processes that had previously been neglected (e.g., the Yarkovsky effect). Collisions have certainly played an important role in the evolution of the Kuiper Belt as well, though only one collisional family has been identified in that region to date, around the dwarf planet Haumea. In this paper, we combine insights into collisional families from numerical simulations with the current observational constraints on the dynamical structure of the Kuiper Belt to investigate the ideal sizes and locations for identifying collisional families. We find that larger progenitors (r ∼ 500 km) result in more easily identifiable families, given the difficulty in identifying fragments of smaller progenitors in magnitude-limited surveys, despite their larger spread and less frequent occurrence. However, even these families do not stand out well from the background. Identifying families as statistical overdensities is much easier than characterizing families by distinguishing individual members from interlopers. Such identification seems promising, provided the background population is well known. In either case, families will also be much easier to study where the background population is small, i.e., at high inclinations. Overall, our results indicate that entirely different techniques for identifying families will be needed for the Kuiper Belt, and we provide some suggestions.

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Section: Resultsmentioning

confidence: 99%

Identifying Collisional Families in the Kuiper Belt

Marcus

Ragozzine

Murray-Clay

et al. 2011

ApJ

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“…Spatial point processes are the stochastic models generating such data. We refer to Stoyan et al (1995), Illian et al (2008) or Møller and Waagepetersen (2004) for an overview on spatial point processes. The Poisson point process is the reference process to model random locations of points without interaction.…”

Section: Introductionmentioning

confidence: 99%

“…Many alternative models such as Cox point processes (including Neymann-Scott processes, shot noise Cox processes, log-Gaussian Cox processes) or Gibbs point processes allow us to introduce clustering effects or to produce regular patterns (see again e.g. Møller and Waagepetersen (2004) or Illian et al (2008)). First introduced by Macchi (1975), the interesting class of determinantal point processes has been revisited recently by Lavancier et al (2015) in a statistical context.…”

Section: Introductionmentioning

confidence: 99%

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Standard and robust intensity parameter estimation for stationary determinantal point processes

Coeurjolly

Biscio

2016

Spatial Statistics

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This work is concerned with the estimation of the intensity parameter of a stationary determinantal point process. We consider the standard estimator, corresponding to the number of observed points per unit volume and a recently introduced median-based estimator more robust to outliers. The consistency and asymptotic normality of estimators are obtained under mild assumptions on the determinantal point process. We illustrate the efficiency of the procedures in a simulation study.

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“…Identificar os fatores que influenciam o padrão espacial das plantas na natureza é de grande importância para o entendimento dos processos ecológicos que atuam sobre a estrutura da distribuição espacial, os quais contribuem para a manutenção da alta diversidade biológica (ILLIAN et al, 2008). Estudos recentes têm avaliado a influência dos fatores abióticos sobre o padrão de distribuição espacial das espécies arbóreas.…”

Section: Introductionunclassified

Fatores abióticos condicionantes da distribuição de espécies arbóreas em quatro formações florestais do Estado de São Paulo

Magalhães¹

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Statistical Analysis and Modelling of Spatial Point Patterns

Cited by 1,148 publications

References 0 publications

Identifying Collisional Families in the Kuiper Belt

Identifying Collisional Families in the Kuiper Belt

Standard and robust intensity parameter estimation for stationary determinantal point processes

Fatores abióticos condicionantes da distribuição de espécies arbóreas em quatro formações florestais do Estado de São Paulo

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