Improving the Computation of Brier Scores for Evaluating Expert-Elicited Judgements

Abstract

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Structured expert judgement (SEJ) is a suite of techniques used to elicit expert predictions, e.g. probability predictions of the occurrence of events, for situations in which data are too expensive or impossible to obtain. The quality of expert predictions can be assessed using Brier scores and calibration questions. In practice, these scores are computed from data that may have a correlation structure due to sharing the effects of the same levels of grouping factors of the experimental design. For example, asking common questions from experts may result in correlated probability predictions due to sharing common question effects. Furthermore, experts commonly fail to answer all the needed questions. Here, we focus on (i) improving the computation of standard error estimates of expert Brier scores by using mixed-effects models that support design-based correlation structures of observations, and (ii) imputation of missing probability predictions in computing expert Brier scores to enhance the comparability of the prediction accuracy of experts. We show that the accuracy of estimating standard errors of expert Brier scores can be improved by incorporating the within-question correlations due to asking common questions. We recommend the use of multiple imputation to correct for missing data in expert elicitation exercises. We also discuss the implications of adopting a formal experimental design approach for SEJ exercises.

Keywords

• hierarchical data
• mixed-effects models
• random effects
• within-question correlations
• imputation
• experimental design