Elicitation of Probabilities for Belief Networks: Combining Qualitative and Quantitative Information

TL;DR

This paper presents a method for eliciting probabilities for belief networks by combining qualitative and quantitative information, using constraints to derive probability distributions without requiring extensive statistical data.

Contribution

It introduces a non-invasive elicitation technique that encodes expert knowledge as constraints and derives probability distributions, addressing challenges in probability estimation.

Findings

Effective integration of qualitative and quantitative info

Can work with limited or non-numeric expert input

Produces probability distributions consistent with expert constraints

Abstract

Although the usefulness of belief networks for reasoning under uncertainty is widely accepted, obtaining numerical probabilities that they require is still perceived a major obstacle. Often not enough statistical data is available to allow for reliable probability estimation. Available information may not be directly amenable for encoding in the network. Finally, domain experts may be reluctant to provide numerical probabilities. In this paper, we propose a method for elicitation of probabilities from a domain expert that is non-invasive and accommodates whatever probabilistic information the expert is willing to state. We express all available information, whether qualitative or quantitative in nature, in a canonical form consisting of (in) equalities expressing constraints on the hyperspace of possible joint probability distributions. We then use this canonical form to derive second-order probability distributions over the desired probabilities.