Expert elicitation of the variogram

N.P. Truong, G.B.M. Heuvelink, J.P. Gosling

Research output: Chapter in Book/Report/Conference proceedingAbstract

Abstract

Expert elicitation of the variogram P. Truong, G.B.M. Heuvelink, J.P. Gosling gerard.heuvelink@wur.nl Wageningen University, Department of Environmental Sciences, PO Box 47, 6700 AA Wageningen, Netherlands The variogram is the key instrument of geostatistics. Estimation of the variogram typically relies on a sufficiently large number of observations of the target variable. However, budget constraints may cause that a too sparse data set is used to estimate the variogram, which will impair the subsequent geostatistical analysis. In some cases it may even be impossible to collect observations to estimate the variogram, such as when in scenario studies the spatial variability of a variable defined in the future is to be assessed. In addition, prior information about the variogram may also be very useful to design an optimal sampling scheme in field surveys and in Bayesian geostatistics. It is, therefore, sensible to explore approaches to estimate the variogram other than through a structural analysis of observations. In this paper we explore how the variogram can be elicited from experts. Experts can be very knowledgeable about the spatial variability of target variables, but directly asking experts about the nugget, sill, range and shape of the variogram may not be sensible because many experts are not familiar with these concepts. The variogram is typically estimated by the average squared increments of the target variable over various lags, but robust estimation of the variogram uses the median of the absolute differences of the target variable over distances. Statistical expert elicitation is well developed to extract the median of uncertain quantities from experts. Thus, the median of the absolute increment is a sensible target quantity of the elicitation procedure. We developed an expert elicitation methodology on this principle, by eliciting the median for multiple separation distances and fitting a variogram. First, a protocol of a well-structured elicitation procedure was designed. Next a web-based tool for online elicitation was built that is composed of three main components: (1) web-GIS interface for elicitation and feedback, (2) statistical calculation and mathematical aggregation to merge the opinions of multiple experts and (3) database management. The prototype was tested and evaluated in a case study on elicitation of the variogram of soil pH. The evaluation showed that the online elicitation tool is satisfactory, although currently it is only a prototype that needs to be further developed.
Original languageEnglish
Title of host publicationPedometrics 2011 - Innovations in Pedometrics; Book of abstracts, August 30 - September 2, 2011, Prague, Czech Republic
EditorsO. Jaksik, A. Klement, L. Boruvka
Place of PublicationPrague
PublisherCzech University of Life Sciences
Pages48
ISBN (Print)9788021321953
Publication statusPublished - 2011
EventPedometrics 2011 -
Duration: 30 Aug 20112 Sep 2011

Conference

ConferencePedometrics 2011
Period30/08/112/09/11

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