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Spatial Point Processes (spatial + point_process)

Distribution by Scientific Domains

Mathematics and Statistics	100%

Selected Abstracts

Estimating the Intensity of a Spatial Point Process from Locations Coarsened by Incomplete Geocoding

BIOMETRICS, Issue 1 2008
Dale L. Zimmerman
Summary The estimation of spatial intensity is an important inference problem in spatial epidemiologic studies. A standard data assimilation component of these studies is the assignment of a geocode, that is, point-level spatial coordinates, to the address of each subject in the study population. Unfortunately, when geocoding is performed by the standard automated method of street-segment matching to a georeferenced road file and subsequent interpolation, it is rarely completely successful. Typically, 10,30% of the addresses in the study population, and even higher percentages in particular subgroups, fail to geocode, potentially leading to a selection bias, called geographic bias, and an inefficient analysis. Missing-data methods could be considered for analyzing such data; however, because there is almost always some geographic information coarser than a point (e.g., a Zip code) observed for the addresses that fail to geocode, a coarsened-data analysis is more appropriate. This article develops methodology for estimating spatial intensity from coarsened geocoded data. Both nonparametric (kernel smoothing) and likelihood-based estimation procedures are considered. Substantial improvements in the estimation quality of coarsened-data analyses relative to analyses of only the observations that geocode are demonstrated via simulation and an example from a rural health study in Iowa. [source]

Inference for Clustered Inhomogeneous Spatial Point Processes

BIOMETRICS, Issue 2 2009
P. A. Henrys
Summary We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K -function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. [source]

A Model-Based Approach for Making Ecological Inference from Distance Sampling Data

BIOMETRICS, Issue 1 2010
Devin S. Johnson
Summary We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike's information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function. [source]

Residual analysis for spatial point processes (with discussion)

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2005
A. Baddeley
Summary., We define residuals for point process models fitted to spatial point pattern data, and we propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, kernel smoothed intensity and Berman's diagnostic) are recovered as special cases. Diagnostic tools are developed systematically, by using an analogy between our spatial residuals and the usual residuals for (non-spatial) generalized linear models. The conditional intensity , plays the role of the mean response. This makes it possible to adapt existing knowledge about model validation for generalized linear models to the spatial point process context, giving recommendations for diagnostic plots. A plot of smoothed residuals against spatial location, or against a spatial covariate, is effective in diagnosing spatial trend or co-variate effects. Q,Q -plots of the residuals are effective in diagnosing interpoint interaction. [source]