An FDA-Based Approach for Clustering Elicited Expert Knowledge

Abstract

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

Keywords

• expert knowledge elicitation
• functional data analysis
• Hellinger distance
• hierarchical clustering