Juergen Pilz

Network optimization algorithms and scenarios in the context of automatic mapping

Many different algorithms can be used to optimize the design of spatial measurement networks. For the spatial interpolation of environmental variables in routine and emergency situations, computation time and interpolation accuracy are important criteria to evaluate and compare algorithms. In many practical situations networks are not designed from scratch but instead the objective is to modify an existing network. The goal then is to add new measuring stations optimally or to withdraw existing stations with as little damage done as possible. The objective of this work is to compare the performance of different optimization algorithms for both computation time and accuracy criteria. We describe four algorithms and apply these to three datasets. In all scenarios the mean universal kriging variance (MUKV) is taken as the interpolation accuracy measure. Results show that greedy algorithms that minimize the information entropy perform best, both in computing time and optimality criterion.

Homogeneous climate regions in Pakistan

In this study, monthly average meteorological data and spatial coordinates are supposed to influence the climate variation. The geographical coordinates are transformed by using the Lambert projection method and are combined with the meteorological data. The complete data is standardised with zero mean and unit variance to remove the effect of different measurement scales. Various clustering methods are used to aggregate data, which are close in space and have similar climate. In our case, medoids clustering algorithm provides good separation and aggregation properties and if Lambert coordinates are used.

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

Recently, Spock and Pilz [38], 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 Spock and Pilz [38] 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 [37] 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.

Smoothing Cancer Ratios in Tirol: A Bayesian Model in Epidemiology

We analyse lung-cancer data on men from 278 irregularly shaped municipalities in a county of Austria where the number of inhabitants is varying from 50 to over 118,000. Data consists of observed incidence and mortality counts in 18 age-groups for the period from 1988 to 1992. To smooth the ratios we focus on a Bayesian modelling approach which incorporates geographical variation in the model so that less reliable estimates are drawn towards a local mean. Full Bayesian analysis is done via Gibbs sampling. Maps of the estimated ratios are drawn and found to be smoother. Credible intervals for the full Bayesian estimate of relative risk show that only one of the regions with high crude ratios seems to have a posterior risk higher than one.