Optimal design for detecting dependencies with an application in spatial ecology

Authors


  • This article is published in Environmetrics as a special issue on Spatio-Temporal Stochastic Modelling (METMAV), edited by Wenceslao González-Manteiga and Rosa M. Crujeiras, University of Santiago de Compostela, Spain.

Werner G. Müller, Johannes Kepler University Linz, Austria. E-mail: werner.mueller@jku.at

Abstract

The paper is concerned with further developing a spatial sampling method based upon optimal design concepts motivated by an application in the area of biodiversity monitoring. Statistical techniques for detecting spatial patterns in the distribution of species richness now have some long tradition in this field, specifically the use of correlograms. The issue of where (and when) to undertake observations has, but only rarely, been treated. In this paper, we aim to extend the existing literature with techniques of finding good designs to optimize the power of tests for spatial dependence. Special emphasis will be given to the difference in using the exact distribution of Moran's math formula and its normal approximation in this context. We uncover the remarkable effect that the use of optimal designs tends to improve the normal approximation. Two illustrative artificial examples will be followed by a real case analysis from the ecological literature. Copyright © 2011 John Wiley & Sons, Ltd.

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