On the elicitation of continuous, symmetric, unimodal distributions

TL;DR

This paper discusses challenges in fitting continuous, symmetric, unimodal distributions to expert judgments, emphasizing the importance of careful fitting and feedback to accurately reflect expert beliefs.

Contribution

It highlights potential pitfalls in distribution fitting, demonstrating how a Cauchy distribution can be mistaken for a normal distribution in expert elicitation.

Findings

Fitting a Cauchy distribution to normal beliefs is possible.

Careful feedback is necessary to ensure accurate distribution fitting.

Abstract

In this brief note, we highlight some difficulties that can arise when fitting a continuous, symmetric, unimodal distribution to a set of expert's judgements. A simple analysis shows it is possible to fit a Cauchy distribution to an expert's beliefs when their beliefs actually follow a normal distribution. This example stresses the need for careful distribution fitting and for feedback to the expert about what the fitted distribution implies about their beliefs.