in the analysis of spatial point patterns, complete spatial randomness (csr) hypothesis,which is a restriction of a homogenous poisson process to study region a, operates as a dividinghypothesis between “regular” and “aggregated” patterns. meanwhile, many alternatives to csr inaggregated patterns are extensions of homogenous poisson processes themselves. therefore, when thecsr hypothesis is rej...

To test for “randomness” in spatial point patterns, we propose two test statistics that are obtained by “reducing” two-dimensional point patterns to the one-dimensional one. Also the exact and asymptotic distribution of these statistics are drawn.

to test for “randomness” in spatial point patterns, we propose two test statistics that are obtained by “reducing” two-dimensional point patterns to the one-dimensional one. also the exact and asymptotic distribution of these statistics are drawn.

In looking at ecological processes, interest in the pattern of occurrences of species, e.g., the pattern of trees in a forest, say junipers and pinions. In spatial epidemiology, we seek to find pattern in disease cases, perhaps different patterns for cases vs. controls. Exple: breast cancer cases; treatment option mastectomy or radiation In syndromic surveillance we seek to identify disease out...

Traditional kernel methods for estimating the spatially-varying density of points in a spatial point pattern may exhibit unrealistic artefacts, addition to familiar problems bias and over- or under-smoothing. Performance can be improved by using diffusion smoothing, which smoothing is heat on domain. This paper develops into practical statistical methodology two-dimensional data. We clarify adv...