The phoropter method: a stochastic graphical procedure for prior elicitation in univariate data models

Common methods for Bayesian prior elicitation call for expert belief in the form of numerical summaries. However, certain challenges remain with such strategies. Drawing on recent advances made in graphical inference, we propose an interactive method and tool for prior elicitation in which experts express their belief through a sequence of selections between pairs of graphics, reminiscent of the common procedure used during eye examinations. The graphics are based on synthetic datasets generated from underlying prior models with carefully chosen parameters, instead of the parameters themselves. At each step of the process, the expert is presented with two familiar graphics based on these datasets, billed as hypothetical future datasets, and makes a selection regarding their relative likelihood. Underneath, the parameters that are used to generate the datasets are generated in a way that mimics the Metropolis algorithm, with the experts' responses forming transition probabilities. Using the general method, we develop procedures for data models used regularly in practice: Bernoulli, Poisson, and Normal, though it extends to additional univariate data models as well. A free, open-source Shiny application designed for these procedures is also available online, helping promote best practice recommendations in myriad ways. The method is supported by simulation.