Balancing the Elicitation Burden and the Richness of Expert Input When Quantifying Discrete Bayesian Networks

Abstract

Structured expert judgment (SEJ) is a method for obtaining estimates of uncertain quantities from groups of experts in a structured way designed to minimize the pervasive cognitive frailties of unstructured approaches. When the number of quantities required is large, the burden on the groups of experts is heavy, and resource constraints may mean that eliciting all the quantities of interest is impossible. Partial elicitations can be complemented with imputation methods for the remaining, unelicited quantities. In the case where the quantities of interest are conditional probability distributions, the natural relationship between the quantities can be exploited to impute missing probabilities. Here we test the Bayesian intelligence interpolation method and its variations for Bayesian network conditional probability tables, called “InterBeta.” We compare the various outputs of InterBeta on two cases where conditional probability tables were elicited from groups of experts. We show that interpolated values are in good agreement with experts' values and give guidance on how InterBeta could be used to good effect to reduce expert burden in SEJ exercises.

A flexible method for parameterizing ranked nodes in Bayesian networks using Beta distributions

“…The Icombination function can be changed, however the default option is the arithmetic mean. 14 We note however that Barons et al (2021) find evidence that the geometric mean may often be a better choice. The I-combined values are normalized to fall into the range [0,1], and these normalized values are the row weights.…”

“…We now present an example of how InterBeta can be applied to a very simple problem, showing how the inputs might be elicited and what kind of outputs can be generated for each of the different methods. We do not provide a performance analysis here, but an in-depth analysis of the performance and the corresponding implications for trading off elicitation burden against CPT fidelity can be found in Barons et al (2021).…”

“…We do not provide a performance analysis here, but an in‐depth analysis of the performance and the corresponding implications for trading off elicitation burden against CPT fidelity can be found in Barons et al. (2021). For simplicity of illustration, in all the following cases, the I‐combination function is the arithmetic mean.…”

“…3 2 A freely available implementation can be found at https://bayesian-intelligence.com/ interpolator/. 3 An evaluation of the method is provided by Barons et al (2021) in this issue.…”

A Bayesian Modelling Framework for Integration of Ecosystem Services into Freshwater Resources Management

“…In a BBN, as the number of connections to an individual node increases, the number of parameters needed also increases multiplicatively. Considerable work has been done on efficient methods for deriving large numbers of conditional probability values, (Das 2004) who, while recognising the subjective nature of experts' experiences and opinions, derived a weighted sum approach with a linear increase in complexity for additional connections to nodes, and more recently in a two stage approach that allows experts establish an initial approximate CPT and subsequently refine it (Hassall et al 2019) and in a Bayesian inference approach applied to a partial analysis, (Barons et al 2021). These techniques were not needed here, as we had sufficient time to elicit most of the CPT information directly from the experts, or from measured data.…”