Citizens’ beliefs about uncertain events are fundamental variables in many areas of political science. While beliefs are often conceptualized in the form of distributions, obtaining reliable measures in terms of full probability densities is a difficult task. In this letter, we ask if there is an effective way of eliciting beliefs as distributions in the context of online surveys. Relying on experimental evidence, we evaluate the performance of five different elicitation methods designed to capture citizens’ uncertain expectations. Our results suggest that an elicitation method originally proposed by Manski (2009) performs well. It measures average citizens’ subjective belief distributions reliably and is easily implemented in the context of regular (online) surveys. We expect that a wider use of this method will lead to considerable improvements in the study of citizens’ expectations and beliefs.

The generalized linear model (GLM) is a statistical model which has been widely used in actuarial practices, especially for insurance ratemaking. Due to the inherent longitudinality of property and casualty insurance claim datasets, there have been some trials of incorporating unobserved heterogeneity of each policyholder from the repeated observations. To achieve this goal, random effects models have been proposed, but theoretical discussions of the methods to test the presence of random effects in GLM framework are still scarce. In this article, the concept of Bregman divergence is explored, which has some good properties for statistical modeling and can be connected to diverse model selection diagnostics as in Goh and Dey [(2014) Journal of Multivariate Analysis, 124, 371–383]. We can apply model diagnostics derived from the Bregman divergence for testing robustness of a chosen prior by the modeler to possible misspecification of prior distribution both on the naive model, which assumes that random effects follow a point mass distribution as its prior distribution, and the proposed model, which assumes a continuous prior density of random effects. This approach provides insurance companies a concrete framework for testing the presence of nonconstant random effects in both claim frequency and severity and furthermore appropriate hierarchical model which can explain both observed and unobserved heterogeneity of the policyholders for insurance ratemaking. Both models are calibrated using a claim dataset from the Wisconsin Local Government Property Insurance Fund which includes both observed claim counts and amounts from a portfolio of policyholders.

Objectives: Ongoing developments in design have improved the outlook for left-ventricular assist device (LVAD) implantation as a therapy in end-stage heart failure. Nevertheless, early cost-effectiveness assessments, based on first-generation devices, have not been encouraging. Against this background, we set out (i) to examine the survival benefit that LVADs would need to generate before they could be deemed cost-effective; (ii) to provide insight into the likelihood that this benefit will be achieved; and (iii) from the perspective of a healthcare provider, to assess the value of discovering the actual size of this benefit by means of a Bayesian value of information analysis.

Methods: Cost-effectiveness assessments are made from the perspective of the healthcare provider, using current UK norms for the value of a quality-adjusted life-year (QALY). The treatment model is grounded in published analyses of the Randomized Evaluation of Mechanical Assistance for the Treatment of Congestive Heart Failure (REMATCH) trial of first-generation LVADs, translated into a UK cost setting. The prospects for patient survival with second-generation devices is assessed using Bayesian prior distributions, elicited from a group of leading clinicians in the field.

Results: Using established thresholds, cost-effectiveness probabilities under these priors are found to be low (∼.2 percent) for devices costing as much as £60,000. Sensitivity of the conclusions to both device cost and QALY valuation is examined.

Conclusions: In the event that the price of the device in use would reduce to £40,000, the value of the survival information can readily justify investment in further trials.