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An FDA-Based Approach for Clustering Elicited Expert Knowledge

Author

Listed:
  • Carlos Barrera-Causil

    (Grupo de Investigación Davinci, Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano -ITM-, Medellín 050034, Colombia)

  • Juan Carlos Correa

    (Escuela de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia sede Medellín, Medellín 050034, Colombia)

  • Andrew Zamecnik

    (Centre for Change and Complexity in Learning, The University of South Australia, Adelaide 5000, Australia)

  • Francisco Torres-Avilés

    (Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Santiago 9170020, Chile
    We dedicate this work to Prof Torres-Avilés’s memory. He was part of the conceptualisation behind this work and was always committed to see the work through.)

  • Fernando Marmolejo-Ramos

    (Centre for Change and Complexity in Learning, The University of South Australia, Adelaide 5000, Australia)

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.

Suggested Citation

  • Carlos Barrera-Causil & Juan Carlos Correa & Andrew Zamecnik & Francisco Torres-Avilés & Fernando Marmolejo-Ramos, 2021. "An FDA-Based Approach for Clustering Elicited Expert Knowledge," Stats, MDPI, vol. 4(1), pages 1-21, March.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:1:p:14-204:d:510339
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    References listed on IDEAS

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