Web-based tool for expert elicitation of the variogram

Abstract

The variogram is the keystone of geostatistics. Estimation of the variogram is deficient and difficult when there are no or too few observations available due to budget constraints or physical and temporal obstacles. In such cases, expert knowledge can be an important source of information. Expert knowledge can also fulfil the increasing demand for an a priori variogram in Bayesian geostatistics and spatial sampling optimization. Formal expert elicitation provides a sound scientific basis to reliably and consistently extract knowledge from experts. In this study, we aimed at applying existing statistical expert elicitation techniques to extract the variogram of a regionalized variable that is assumed to have either a multivariate normal or lognormal spatial probability distribution from expert knowledge. To achieve this, we developed an elicitation protocol and implemented it as a web-based tool to facilitate the elicitation of beliefs from multiple experts. Our protocol has two main rounds: elicitation of the marginal probability distribution and elicitation of the variogram. The web-based tool has three main components: a web interface for expert elicitation and feedback; a component for statistical computation and mathematical pooling of multiple experts? knowledge; and a database management component. Results from a test case study show that the protocol is adequate and that the online elicitation tool functions satisfactorily. The web-based tool is free to use and supports scientists to conveniently elicit the variogram of spatial random variables from experts. The source code is available from the journal FTP site under the GNU General Public License.