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Hybrid elicitation and quantile-parametrized likelihood

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  • Perepolkin, Dmytro
  • Goodrich, Benjamin
  • Sahlin, Ullrika

Abstract

This paper extends the application of quantile-based Bayesian inference to probability distributions defined in terms of quantiles of observable quantities. Quantile-parameterized distributions are characterized by high shape flexibility and parameter interpretability, making them useful for eliciting information about observables. To encode uncertainty in the quantiles elicited from experts, we propose a Bayesian model based on the metalog distribution and a variant of the Dirichlet prior. We discuss the resulting hybrid expert elicitation protocol, which aims to characterize uncertainty in parameters by asking questions about observable quantities. We also compare and contrast this approach with parametric and predictive elicitation methods.

Suggested Citation

  • Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "Hybrid elicitation and quantile-parametrized likelihood," OSF Preprints paby6_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:paby6_v1
    DOI: 10.31219/osf.io/paby6_v1
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    References listed on IDEAS

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    1. Martin Crowder, 1992. "Bayesian priors based on a parameter transformation using the distribution function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 405-416, September.
    2. Stuart G. Coles & Jonathan A. Tawn, 1996. "A Bayesian Analysis of Extreme Rainfall Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 463-478, December.
    3. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2023. "The tenets of quantile-based inference in Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Perepolkin, Dmytro & Lindsröm, Erik & Sahlin, Ullrika, 2023. "Quantile-parameterized distributions for expert knowledge elicitation," OSF Preprints tq3an, Center for Open Science.
    5. Fadlalla Elfadaly & Paul Garthwaite, 2013. "Eliciting Dirichlet and Connor–Mosimann prior distributions for multinomial models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 628-646, November.
    6. Jonah Gabry & Daniel Simpson & Aki Vehtari & Michael Betancourt & Andrew Gelman, 2019. "Visualization in Bayesian workflow," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 389-402, February.
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