Sensitivity analysis of Bayesian estimates of value function parameters to priors using imprecise probabilities

The elicitation and quantification of preferences of individuals or 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 inquiries using a parameterized value function. When doing this with Bayesian inference, the specification of a prior can be challenging as it may be difficult to find similar cases to transfer knowledge. This makes it particularly important to be informed about the sensitivity of the results to the choice of the prior. This can be done by computing posteriors for different plausible priors and analyzing differences between them. This is infeasible for a large number of priors. This paper proposes the application of Density Ratio Classes, which sandwich non-normalized prior densities between specified lower and upper functional bounds. In this study, differences among posteriors resulting from priors in such a class are analyzed by comparing marginal posterior credible intervals. We compute “outer” credible intervals that range from the minimum of all lower bounds to the maximum of all upper bounds of marginal posterior credible intervals with the same quantile bounds resulting from the priors in the density ratio class. The methodology is easy to implement and only requires one Markov chain of the posterior resulting from the upper function. We provide an R package “DRclass” that supports such implementations. Theoretical considerations and three case studies provide illustration and guidance about constructing the prior density ratio class. • Knowledge about sensitivity to the prior is important in Bayesian inference. • Imprecise (sets of) priors are ideal for analyzing sensitivity to the prior. • Extending Bayesian inference to imprecise priors is numerically very efficient. • Bounds of cumulative probabilities are useful for elicitation and analysis. • Imprecision did not overwhelmingly widen posteriors of preference model parameters.