Synthetic Priors that Merge Opinion from Multiple Experts

Public policy relies strongly upon expert opinion, especially in risk assessment for rare events. But expert opinion is often inconsistent, both within and between experts. We therefore develop a statistical model for the elicited opinions, and use that to borrow strength across the responses through an exchangeable prior. Several versions of that prior are considered; the most advanced uses covariate information on the experts to characterize their areas of agreement and disagreement, which ultimately allows the estimation of the opinion of a synthetic expert whose covariates are selected by the analyst.This result depends upon a novel technique that incorporates the background information of the expert using hierarchical Dirichlet regression and a latent space model. As an illustration, in October 2008 we elicited opinions on the percentage of the popular vote that presidential candidate Barack Obama would win in North Carolina. Among the respondents, those who were conservative or who had lived in North Carolina for a longer period of time gave systematically lower percentages. Our method enables the analyst to infer the opinion of a respondent with a specified political inclination or number of years of residency.