The Weighted Priors Approach for Combining Expert Opinions in Logistic Regression Experiments

When modeling the reliability of a system or component, it is not uncommon for more than one expert to provide very different prior estimates of the expected reliability as a function of an explanatory variable such as age or temperature. Our goal is to incorporate all information from the experts when choosing a design about which units to test. Bayesian design of experiments has been shown to be very successful for generalized linear models, including logistic regression models. We use this approach to develop methodology for the case where there are several potentially non-overlapping priors under consideration. While multiple priors have been used for analysis in the past, they have never been used in a design context. The Weighted Priors method performs well for a broad range of true underlying model parameter choices and is more robust when compared to other reasonable design choices. We illustrate the method through multiple scenarios and a motivating example. Additional figures for this article are available as Supplementary Materials.