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

Abstract

When novice modelers first attempt to build a Bayesian network, they are often impressed with the intuitive graphical structures that capture their causal understanding. This favorable impression evaporates on proceeding to parameterization. Conditional probability tables (CPT) require parameters for often hundreds of very similar scenarios and specifying them in the absence of data can be overwhelming. The problem is even more severe when eliciting parameters from experts with limited time. Often, there is local structure with fewer parameters that better describes the relationship. Such structures include the Noisy OR, decision trees, and equations. These work well for modelers, but can be an issue for experts and particularly groups of experts. An alternative approach is to elicit only a few CPT rows and interpolate the remainder. This is a promising approach, as it can handle unknown structures and multiple experts, but existing techniques can be limited. Here, we present a flexible approach called InterBeta for performing CPT interpolation with ordered nodes. In the simplest case, just two CPT rows are needed, but this can be easily augmented with further information. The basic approach assumes input independence, but allows dependencies to be reintroduced as required, and can also be combined with other local structures such as decision trees or equations, leaving the interpolator to fill in the gaps. We explain the InterBeta method, describe its capabilities and limitations and how it compares to similar approaches and show how it can trade-off elicitation effort against faithfully representing expert understanding.

Bayesian networks for risk analysis and decision support

“…Mascaro and Woodberry (2022) introduce a flexible method for parameterizing incomplete CPTs using interpolation techniques called InterBeta . The authors build on previously proposed frameworks of parameterizing a local structure to alleviate the burden of parameterizing large CPTs.…”

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

“…InterBeta (Mascaro and Woodberry, 2020) works with ordered (i.e., ranked) or binary nodes, such as the nodes from Fig. 1.…”

“…In addition, while we focus here on cases in which the user supplies two CPT rows (the best and worst case), it is also possible to extend the approach to multirow interpolations. (See Mascaro and Woodberry (2020) for further discussion. )…”

“…In this research, we used and tested the Bayesian intelligence interpolation method and its variants for CPTs called “InterBeta” (Mascaro and Woodberry, 2020). We compare the outputs of InterBeta using two case studies where full CPTs were elicited from groups of experts using the IDEA protocol.…”

“…As described inMascaro and Woodberry (2020), specifying row weights only allows direct dependencies between the inputs and the interpolation score node, not directly to the final Beta distribution node.…”