Parametric Procedures in the Analysis of Replicated Pairwise Interaction Point Patterns

Mateu, Jorge

doi:10.1002/1521-4036(200106)43:3<375::aid-bimj375>3.0.co;2-q

Cited by 11 publications

(8 citation statements)

References 16 publications

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“…Taskinen (2001) used point process priors in a Bayesian analysis of time series of functional brain images. Previous methods for ANOVA of replicated point patterns have pertained mainly to spatial point interaction under the assumption of uniform intensity (Diggle et al, 1991(Diggle et al, , 2000Baddeley et al, 1993;Mateu, 2001). To our knowledge, methods for ANOVA of spatial heterogeneity in replicated point pattern data have yet to appear in the statistical literature.…”

Section: Introductionmentioning

confidence: 99%

Modelling Spatial Intensity for Replicated Inhomogeneous Point Patterns in Brain Imaging

Wager

Coull

Lange

2004

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Pharmacological experiments in brain microscopy study patterns of cellular activ- ation in response to psychotropic drugs for connected neuroanatomic regions. A typical ex- perimental design produces replicated point patterns having highly complex spatial variability. Modelling this variability hierarchically can enhance the inference for comparing treatments. We propose a semiparametric formulation that combines the robustness of a nonparametric kernel method with the efficiency of likelihood-based parameter estimation. In the convenient framework of a generalized linear mixed model, we decompose pattern variation by kriging the intensities of a hierarchically heterogeneous spatial point process. This approximation entails discretizing the inhomogeneous Poisson likelihood by Voronoi tiling of augmented point patterns. The resulting intensity-weighted log-linear model accommodates spatial smoothing through a reduced rank penalized linear spline. To correct for anatomic distortion between subjects, we interpolate point locations via an isomorphic mapping so that smoothing occurs relative to common neuroanatomical atlas co-ordinates. We propose a criterion for choosing the degree and spatial locale of smoothing based on truncating the ordered set of smoothing covariates to minimize residual extra-dispersion. Additional spatial covariates, experimental design factors, hierarchical random effects and intensity functions are readily accommodated in the linear predictor, enabling comprehensive analyses of the salient properties underlying replicated point patterns. We illustrate our method through application to data from a novel study of drug effects on neuronal activation patterns in the brain of rats. Copyright 2004 Royal Statistical Society.

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Section: Introductionmentioning

confidence: 99%

Modelling Spatial Intensity for Replicated Inhomogeneous Point Patterns in Brain Imaging

Wager

Coull

Lange

2004

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Parametric methods use maximum likelihood or pseudo‐likelihood methods to fit the parameters of a point process model. These methods have been employed to fit certain homogeneous point processes such as pairwise interactions (Diggle et al , Mateu ) or Gibbs point processes (Bell and Grunwald ). Non‐parametric methods evaluate differences in summary functions (mainly Ripley's K ‐function) among experimental or observational groups.…”

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confidence: 99%

A new non‐parametric method for analyzing replicated point patterns in ecology

Ramón

Cruz²,

Chacón‐Labella³

et al. 2016

Ecography

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Most ecological studies that involve point pattern analyses are based on a single plot, which prevent the separation of the effects of various processes that could act simultaneously, as well as limiting the conclusions that can be extracted from these studies. However, considering the spatial distribution of individuals in several plots as replicates of the same process could help to differentiate its specific effects from those of other confounding processes. Thus, we introduce a new method for analyzing spatial point patterns that are replicated according to a two‐factorial design. By summarizing the spatial patterns as K‐functions, the proposed method computes the average K‐functions for each level of the two factors (i.e. predictors) and for each combination of levels, before estimating the sum of squared deviations from the overall mean K‐function. Inferences of the strength of the relationship between the predictors, their interaction, and the spatial structure are made based on a non‐parametric bootstrap procedure, which considers the dependency among spatial scales. We illustrate the proposed approach based on an analysis of the effects of altitude (with two levels: low and high) and slope (with two levels: flat and steep slopes) on the spatial pattern of Croton wagneri, a dominant shrub in an Andean dry scrubland. Our method detected a significant effect of the interaction between slope and altitude, which could not have been detected using current point pattern analysis methodology. The prevalence of single‐plot analysis in ecological studies may be due to a lack of familiarity with appropriate methods for replicated point patterns, as well as the greater complexity of these methods and the absence of appropriate software. Our approach can be applied to a significant number of ecological questions while maintaining a simple, understandable, and easily reportable methodological framework.

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“…(, ), Baddeley et al . (), Mateu () and Landau et al . (), but they proposed tests for various hypotheses using summary statistics of the process (see also Baddeley et al .…”

Section: Introductionmentioning

confidence: 99%

“…Borgnat et al (2011), Vogel et al (2011 and Nair et al (2013)), but the problem of estimating and modelling daily demand distribution at every station in a network has not yet been addressed, to the best of our knowledge. From a statistical methodology perspective, we can mention early work on replicated point processes by Diggle et al (1991Diggle et al ( , 2000, Baddeley et al (1993), Mateu (2001) and Landau et al (2004), but they proposed tests for various hypotheses using summary statistics of the process (see also Baddeley et al (2015), chapter 16, andDiggle (2013), chapter 5.4), rather than explicitly estimating the intensity functions of the processes, as we do here. More recent work that does address the intensity function estimation problem was done by Wu et al (2013), Bouzas and Ruiz-Fuentes (2015) and Gervini (2016), but only in the context of univariate, not multivariate, processes as in this paper.…”

Section: Introductionmentioning

confidence: 99%

Exploring Patterns of Demand in Bike Sharing Systems Via Replicated Point Process Models

Gervini

Khanal

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary Understanding patterns of demand is fundamental for fleet management of bike sharing systems. We analyse data from the Divvy system of the city of Chicago. We show that the demand for bicycles can be modelled as a multivariate temporal point process, with each dimension corresponding to a bike station in the network. The availability of daily replications of the process enables non‐parametric estimation of the intensity functions, even for stations with low daily counts, and straightforward estimation of pairwise correlations between stations. These correlations are then used for clustering, revealing different patterns of bike usage.

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Parametric Procedures in the Analysis of Replicated Pairwise Interaction Point Patterns

Cited by 11 publications

References 16 publications

Modelling Spatial Intensity for Replicated Inhomogeneous Point Patterns in Brain Imaging

Modelling Spatial Intensity for Replicated Inhomogeneous Point Patterns in Brain Imaging

A new non‐parametric method for analyzing replicated point patterns in ecology

Exploring Patterns of Demand in Bike Sharing Systems Via Replicated Point Process Models

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