Introduction to Imprecise Probabilities

Chapter 15Elicitation

Michael Smithson

Research School of Psychology, The Australian National University, Canberra, Australia

15.1 Methods and issues

The elicitation of imprecise probabilities is a relatively unexplored topic, and so some parts of this review will draw from work on precise probability judgements. Most methods of eliciting imprecise probabilities fall into three groups: Direct numerical estimates, numerical translations of verbal probability expressions (e.g., ‘somewhat likely’), and evaluations of candidate intervals or bounds. We shall begin by surveying these in turn, elaborating the issues and methods in evaluating judged imprecise probabilities. The section thereafter examines methods for evaluating judged probabilities that can be adapted and applied to imprecise probability judgements. The third section discusses factors that influence probability judgements and ways in which elicitation methods may be matched with the purposes intended to be served by elicitation. The final section provides a guide to further reading on this topic.

Numerical elicitation methods range from simply asking for numerical estimates to inferring such estimates from other indicators. Until recently relatively little work had been done comparing these methods with one another or with other alternatives. The most obvious direct numerical estimation task is to ask for a lower and upper bound on the probability of an event. This is rather problematic because no criterion is given ...