Robust Bayesian Estimation of Value Function Parameters Using Imprecise Priors

Abstract

The elicitation and quantification of preferences of individuals or of aggregated preferences of stakeholders or samples of the population are crucial for decision support.This can be done by statistically evaluating the results of discrete choice or indifference inquiries using a parameterized value function.When doing such analyses with Bayesian inference, the specification of a prior can be challenging as it may be difficult to find similar cases from which knowledge could be transferred.For this reason, robustness of the results of Bayesian inference with respect to prior information is particularly important in this context.To address this problem, in addition to comparing the results for different value functions, we suggest to use imprecise probabilities for the prior of the parameters.This leads to the use of a non-parametric class of priors that is much less constrained compared to a parametric family or even just a finite set of priors.The goal of our study is to analyze how much such classes of priors increase posterior ambiguity.We analyze this problem using synthetic and empirical data and with discrete choice and indifference elicitation to investigate to which degree the reduced sample size requirements of the latter technique is maintained under weaker prior assumptions.As a side effect, we also demonstrate that the additional computational burden for such an analysis is rather small and thus hope that this study can stimulate a wider application of such analyses to improve uncertainty assessment in preference elicitation as well in other fields of research.

Keywords: Decision analysis, Uncertainty modelling, Sensitivity analysis, Preference learning, Imprecise probabilities