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 expertunderstanding.