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Complete spatial randomness (CSR) describes a point process whereby point events occur within a given study area in a completely random fashion. It is synonymous with a homogeneous spatial Poisson process.〔O. Maimon, L. Rokach, ''Data Mining and Knowledge Discovery Handbook'' , Second Edition, Springer 2010, pages 851-852 〕 Such a process is modeled using only one parameter , i.e. the density of points within the defined area. The term complete spatial randomness is commonly used in Applied Statistics in the context of examining certain point patterns, whereas in most other statistical contexts it is referred to the concept of a spatial Poisson process.〔O. Maimon, L. Rokach, ''Data Mining and Knowledge Discovery Handbook'' , Second Edition, Springer 2010, pages 851-852 〕 == Model == Data in the form of a set of points, irregularly distributed within a region of space, arise in many different contexts; examples include locations of trees in a forest, of nests of birds, of nuclei in tissue, of ill people in a population at risk. We call any such data-set a spatial point pattern and refer to the locations as events, to distinguish these from arbitrary points of the region in question. The hypothesis of complete spatial randomness for a spatial point pattern asserts that the number of events in any region follows a Poisson distribution with given mean count per uniform subdivision. The events of a pattern are independently and uniformly distributed over space; in other words, the events are equally likely to occur anywhere and do not interact with each other. "Uniform" is used in the sense of following a uniform probability distribution across the study region, not in the sense of “evenly” dispersed across the study region.〔 L. A. Waller, C. A. Gotway, ''Applied Spatial Statistics for Public Health Data'', volume 1 Wiley Chichester, 2004, pages 119–121, 123–127, 137, 139–141, 146–148, 150–151, 157, 203. 〕 There are no interactions amongst the events, as the intensity of events does not vary over the plane. For example, the independence assumption would be violated if the existence of one event either encouraged or inhibited the occurrence of other events in the neighborhood. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「complete spatial randomness」の詳細全文を読む スポンサード リンク
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