Journal ArticleDOI
Tests of 'Randomness' for Spatial Point Patterns
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In this article, the authors investigated the power of edge-correction for spatial point patterns and found that edge correction can substantially reduce the sampling fluctuations of a statistic and so boost the test power based on it.Abstract:
SUMMARY Tests of "randomness" and methods of edge-correction for spatial point patterns are surveyed. The asymptotic distribution theory and power of tests based on the nearest-neighbour distances and estimates of the variance function are investigated. A MAP of small objects is often described as "random" if it is consistent with the null hypothesis of a binomial or Poisson process. The usual first step in the analysis of such a pattern is a test of this null hypothesis; indeed the analysis is often confined to quoting a test statistic or its significance level as a "measure of non-randomness". The aim of this paper is to investigate the power of such tests, particularly tests based on nearest-neighbour distances, interpoint distances and estimators of moment measures, and to assess the efficiency of various corrections for edge-effects. One interesting conclusion is that edge-correction such as applied in the k of Ripley (1977) can substantially reduce the sampling fluctuations of a statistic and so boost the power of a test based on it.read more
Citations
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Journal ArticleDOI
Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems
Jon C. Helton,Freddie J. Davis +1 more
TL;DR: The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol' variance decomposition, and fast probability integration.
Journal ArticleDOI
Survey of sampling-based methods for uncertainty and sensitivity analysis
TL;DR: Sampling-based methods for uncertainty and sensitivity analysis are reviewed and special attention is given to the determination of sensitivity analysis results.
Journal ArticleDOI
Rings, circles, and null-models for point pattern analysis in ecology
Thorsten Wiegand,Kirk A. Moloney +1 more
TL;DR: It is demonstrated that large-scale heterogeneity of a point-pattern biases Ripley's K-function at smaller scales, and it is shown that it can be removed when applying methods that account for first-order effects.
Journal ArticleDOI
Direct visualization of ras proteins in spatially distinct cell surface microdomains
TL;DR: It is found that an inner-plasma membrane lipid raft marker displays cholesterol-dependent clustering in microdomains with a mean diameter of 44 nm that occupy 35% of the cell surface, illustrating that the inner plasma membrane comprises a complex mosaic of discrete micro domains.
ReportDOI
Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems
Jon C. Helton,Freddie J. Davis +1 more
TL;DR: The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol’ variance decomposition, and fast probability integration.
References
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Journal ArticleDOI
Distance to Nearest Neighbor as a Measure of Spatial Relationships in Populations
Philip J. Clark,Francis C. Evans +1 more
TL;DR: In this article, the authors studied the vulnerability of several species to trapping on the islands and found that the islands appeared to lag behind the mainland in the development of their populations and the populations of small mammals fluctuate quite widely and the several populations appear to be somewhat independent of each other.
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The Second-Order Analysis of Stationary Point Processes
TL;DR: In this paper, the authors provide a rigorous foundation for the second-order analysis of stationary point processes on general spaces, including the line and hyperplane processes of Davidson and Krickeberg.
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The spectral analysis of two-dimensional point processes
TL;DR: In this paper, the spectral analysis of two-dimensional stationary point processes (e.g. two Cartesian space co-ordinates x and y, denoted by the vector r) is considered, where r denotes the cumulative number of points at r.
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Boundary-crossing probabilities for the Brownian motion and poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test
TL;DR: In this paper, the first-passage distribution functions of a Brownian motion process are approximated by linear recursions whose coefficients are estimated by linearizing the boundaries within subintervals.
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A note on Strauss's model for clustering
Frank Kelly,B. D. Repley +1 more
TL;DR: In this paper, the authors show how Strauss's model for clustering arises naturally from a family of finite point processes with a Markov property and as the equilibrium distributions of certain Markov processes.