An FDA-based approach for clustering expert knowledge

Representing and analyzing expert knowledge are two complex tasks, and eliciting such knowledge can be used to obtain an individual representation of beliefs for each expert in the form of a probability distribution or function. Such functions are analyzed using statistical tools, but, in many cases, the elicited distributions or experts’ opinion differ. Therefore, appropriate techniques must be used to take into account those discrepancies. In this paper, we propose a hierarchical method for clustering elicited distributions that can be easily extended to functional data. We first transform the infinite-dimensional problem into a finite-dimension alone. Subsequently, we use the Hellinger distance to compute the distances between curves and thus obtain a hierarchical clustering structure. A simulation study was conducted to compare the performance of our proposal with that of thek-meansand agglomerative nesting algorithms. The results show that the method we propose performs better than its counterparts in almost all the situations considered in this study. Finally, an illustration, created using elicited distributions of experts, shows that this kind of technique is essential to understand the point of view of each expert.