Correct testing of mark independence for marked point patterns

Spatial pattern analysis provides valuable information on ecological processes. Many ecological systems can be described by marked point processes. One of the key issues in the statistical application of marked point processes is the question of spatial correlations of the marks. Therefore, the first step of analysis is a test of independence of marks. Many researchers use for this purpose the popular envelope test. However, this may lead to unreasonably high type I error probabilities, because in this test spatial correlations are inspected for a range of distances simultaneously. The paper discusses in detail the use of deviation tests for testing hypotheses of mark independence. Additionally, it demonstrates how the envelope test can be refined so that it becomes a valuable tool both for statistical inference and for understanding the reasons of possible rejections of the independence hypothesis. Two examples from forest ecology illustrate the application of both test types.

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