Design of spatial experiments: Model fitting and prediction

Recently, Spöck and Pilz (2010), demonstrated that the spatial sampling design problem for the Bayesian linear kriging predictor can be transformed to an equivalent experimental design problem for a linear regression model with stochastic regression coefficients and uncorrelated errors. The stochastic regression coefficients derive from the polar spectral approximation of the residual process. Thus, standard optimal convex experimental design theory can be used to calculate optimal spatial sampling designs. The design functionals considered in Spöck and Pilz (2010) did not take into account the fact that kriging is actually a plug-in predictor which uses the estimated covariance function. The resulting optimal designs were close to space-filling configurations, because the design criterion did not consider the uncertainty of the covariance function. In this paper we also assume that the covariance function is estimated, e.g., by restricted maximum likelihood (REML). We then develop a design criterion that fully takes account of the covariance uncertainty. The resulting designs are less regular and space-filling compared to those ignoring covariance uncertainty. The new designs, however, also require some closely spaced samples in order to improve the estimate of the covariance function. We also relax the assumption of Gaussian observations and assume that the data is transformed to Gaussianity by means of the Box-Cox transformation. The resulting prediction method is known as trans-Gaussian kriging. We apply the (Smith and Zhu, 2004) approach to this kriging method and show that resulting optimal designs also depend on the available data. We illustrate our results with a data set of monthly rainfall measurements from Upper Austria.

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“…Actually, Fedorov (1996) was the first to do this. He made use of the so-called Karhunen-Loeve approximation to the error process.…”

Section: Bayesian Spatial Linear Model and Classical Experimental Desmentioning

confidence: 99%

Incorporating covariance estimation uncertainty in spatial sampling design for prediction with trans-Gaussian random fields

Spöck

Pilz

2015

Front. Environ. Sci.

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“…È½M ¼ Àlog det M), where the classical sensitivity function is just the ratio of the prediction variance with the estimated parameter to the prediction variance with the true parameter (cf. Fedorov, 1996). The sensitivity function to be used in an exchange type algorithm can be written as …”

Section: A Heuristic Algorithmmentioning

confidence: 99%

A comparison of spatial design methods for correlated observations

Müller

2005

Environmetrics

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SUMMARYRandom fields are frequently used to model spatial environmental processes. Optimum design theory for regression experiments is consequently employed to assess and construct monitoring networks for these processes. However, straightforward application of much of this theory is not possible, since the typical assumption of independent errors is violated. In the present article I intend to give an overview on design methods that attempt to cope with the problem, amongst them two recently developed approaches. For a comparison the techniques will be applied to the design of a water-quality monitoring network in the Südliche Tullnerfeld in Lower Austria.

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“…For instance, we do not introduce a distance between two points xi and xi' (c.f. Fedorov (1996)). The concept of a distance is much less natural in communication network measurements than in meteorology or seismology, where the physical distance 11 xi -xi' 11 between observing stations may define the behavior of elements K(xi,xir) of the matrix K as functions of 11 xi -xit 11.…”

Section: Model and Optimality Criteriamentioning

confidence: 99%

Optimal monitoring of computer networks

Fedorov¹,

Flanagan²

1998

Institute of Mathematical Statistics Lecture Notes - Monograph Series

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We apply the ideas from optimal design theory to the very specific area of monitoring large computer networks. The behavior of these networks is so complex and uncertain that it is quite natural to use the statistical methods of experimental design which were originated in such areas as biology, behavioral sciences and agriculture, where the random character of phenomena is a crucial component and systems are too complicated to be described by some sophisticated deterministic models. We want to emphasize that only the f i s t steps have been completed, and relatively simple underlying concepts about network functions have been used. Our immediate goal is to initiate studies focused on developing efficient experimental design techniques which can be used by practitioners working with large networks operating and evolving in a random environment.

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Design of spatial experiments: Model fitting and prediction

Abstract: This report has been reproduced directly from the best available copy.

Cited by 24 publications

References 6 publications

Incorporating covariance estimation uncertainty in spatial sampling design for prediction with trans-Gaussian random fields

Incorporating covariance estimation uncertainty in spatial sampling design for prediction with trans-Gaussian random fields

A comparison of spatial design methods for correlated observations

Optimal monitoring of computer networks

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