Paul H. Garthwaite and Anthony O'Hagan
University of Aberdeen and University of Sheffield
Publication details: The Statistician 49, 455-477, 2000.
This paper reports an experiment in which thirty-two experts at three water companies quantified their opinions about two problems, the cost of refurbishing specified pumping stations and the length of unrecorded S24 sewers in four towns. Medians and both unconditional and conditional assessments of quantiles were elicited and assessments were compared with reality and given scores. The quantiles that experts were asked to assess varied, as did the extent of the experts' relevant background knowledge, and the influences of these factors on standard deviations and scores are examined. The main focus is on modelling approaches to use the elicited assessments to form subjective probability distributions. We consider fitting lognormal distributions to model asymmetric distributions and also examine models to relate a quantity's assessed standard deviation and inter-quantile range to its size, finding that inter-quantile ranges can be modelled more accurately. In addition, different approaches to separating opinions about components of variance are evaluated and compared.
Keywords: Assessment tasks; Elicitation tools; Prior probability; Quantiles; Subjective opinion; Variance-components.