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.
Highlights
Even when we receive information under the same conditions, our point of view may greatly differ from others’
To test the efficiency of the clustering algorithm our method, we propose a hierarchical clustering technique for functional data and compare it, via statistical simulation, with functional k-means, Ward’s, and average linkage methods (these methods are implemented in R [23] through thekmeans.fd function in the fda.usc package (Febrero-Bande and Oviedo, 2012) [24] and the agnes function in the cluster package [25]
To examine the similarity between two clusters, we considered the Rand index, the Fowlkes–Mallows index, the Jaccard coefficient—index to measure similarity between sample sets—and the correct classification rate (Hubert and Arabie, 1985; Morlini and Zani, 2012) [26,27]
Summary
Even when we receive information under the same conditions, our point of view may greatly differ from others’. We can adopt the Delphi method as an elicitation method The latter is defined by Brown (1968) [1] as a technique based on the results of multiple rounds of questionnaires sent to a panel of experts and whose purpose is to reach a consensus on their opinion. Such method is effective, as it allows a group of individuals to address a complex problem and could be implemented to obtain a single representation of experts’
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