A quantitative study of quantile based direct prior elicitation from expert opinion

Abstract

Eliciting priors from expert opinion enjoys more efficiency and reliability by avoiding the statistician's potential subjectivity. Since elicitation on the predictive prior probability space requires too-simple priors and may be burdened with additional uncertainties arising from the response model, quantitative elicitation of flexible priors on the direct prior probability space deserves much attention. Motivated by precisely acquiring the shape information for the general location-scale-shape family beyond the limited and simple location-scale family, we investigate multiple numerical procedures for a broad class of priors, as well as interactive graphical protocols for more complicated priors. We highlight the quantile based approaches from several aspects, where Taylor's expansion is demonstrated to be an efficient approximate alternative to work on the regions in which the shape parameter is highly sensitive. By observing inherent associations between the scale and shape parameters, we put more weight on practical solutions under a proper sensitivity index (SI) rather than presumability. Our proposed methodology is demonstrated through skew-normal and Gamma hyper-parameter elicitation where the shape parameter is numerically solved in a stable way. The performance comparisons among different elicitation approaches are also provided.