Expert elicitation of the variogram Phuong N. Truong Gerard B.M. Heuvelink John Paul Gosling Wageningen University (NL) Food and Environmental Research Agency (UK) Pedometrics 2011

It is a measure of spatial variability of soil properties It is required for kriging and spatial stochastic simulation The variogram is a key tool in pedometrics But it is not always available: At least 200 observations are required to estimate it reliably (perhaps 60 will do) In many cases this may be too expensive or otherwise impossible

ASK EXPERTS! What else can we do to estimate the variogram? But how should expert information be derived? We often read “...was derived using expert knowledge...”, without further explanation But much can go wrong when consulting experts Must therefore make use of formal and established procedures: expert elicitation

Aims to construct a probability distribution that properly represents the expert’s knowledge Scientific field in its own right, many text books, conferences and journals Involves contributions from statistics and psychology (understanding human judgement) Expert elicitation

1.Background and preparation 2.Identify and recruit expert(s) 3.Motivating and training the expert(s), e.g. to avoid overconfidence and anchoring 4.Structuring and decomposition (ensure that expert agrees with how the problem is structured) 5.The elicitation itself 6.Assess the adequacy of the elicitation Expert elicitation procedure involves six steps

Closer look at step 5 in case of elicitation of a univariate continuous distribution by multiple experts:

1.Choose lags for which the semivariance is to be elicited 2.Elicit semivariance for each lag using Cressie’s robust estimator: Our approach to expert elicitation of the variogram 3.Fit variogram using least squares 4.Show simulated realisations along transect and allow expert to modify their judgement 5.Pool variograms of multiple experts using mathematical aggregation

Expert  Geostatistician Cannot ask: What are the nugget, sill, range and shape of the variogram? Can ask:

Summary of variogram elicitation procedure

Let’s try a live demo (but screendumps prepared as a back-up) Web-based implementation at

Expert elicitation of variograms is possible but takes a lot of effort Web-based tool ready to be used, feel free to try it out at No real case study yet, but we plan to elicit the variogram of soil pH for a region in the UK Variogram elicitation useful in case of too few or no data, and also for: –Spatial sample design optimization for minimization of the average (universal) kriging variance (Brus & Heuvelink, Geoderma 138, pp ) –Use as a prior in Bayesian estimation of the variogram Conclusions

Thank you!

Starting page

Round 1: marginal distribution

Feedback round 1

First page round 2

Elicitation of semivariance at seven lags

Feedback by simulated reality along transect