Calibrating expert assessments using hierarchical Gaussian process models

Abstract

Expert assessments are routinely used to inform management and other decision making. However, often these assessments contain considerable biases and uncertainties for which reason they should be calibrated if possible. Moreover, coherently combining multiple expert assessments into one estimate poses a long-standing problem in statistics since modeling expert knowledge is often difficult. Here, we present a hierarchical Bayesian model for expert calibration in a task of estimating a continuous univariate parameter. The model allows experts' biases to vary as a function of the true value of the parameter and according to the expert's background. We follow the fully Bayesian approach (the so-called supra-Bayesian approach) and model experts' bias functions explicitly using hierarchical Gaussian processes. We show how to use calibration data to infer the experts' observation models with the use of bias functions and to calculate the bias corrected posterior distributions for an unknown system parameter of interest. We demonstrate and test our model and methods with simulated data and a real case study on data-limited fisheries stock assessment. The case study results show that experts' biases vary with respect to the true system parameter value and that the calibration of the expert assessments improves the inference compared to using uncalibrated expert assessments or a vague uniform guess. Moreover, the bias functions in the real case study show important differences between the reliability of alternative experts. The model and methods presented here can be also straightforwardly applied to other applications than our case study.