Processing unreliable judgements with an imprecise hierarchical model

Abstract

In processing expert judgements, it is common to assign experts’ opinions different degrees of plausibility or probability. This results in the necessity of constructing some kind of hierarchical model. Hierarchical models are widely used in Bayesian inference. Several models have been proposed by the adherents of imprecise statistical reasoning. This paper describes a new hierarchical uncertainty model of a more general form: first- and second-order uncertainty models are both imprecise. We demonstrate that depending on what kind of evidence the modeller has at hand and the reliability quantifying the quality of expert judgement one comes to different rules of combination. It is shown that the rules of combination known in imprecise statistical reasoning can be inferred from the approach proposed in the paper. We describe how the model can be used to generate first-order coherent interval-valued previsions. The paper is concluded by addressing the issue of computing the probability of an event ‘one imprecise value is greater than another’. This case is prominent in light of decision making based on imprecise previsions.