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The tenets of quantile-based inference in Bayesian models

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

Abstract

Bayesian inference can be extended to probability distributions defined in terms of their inverse distribution function, i.e. their quantile function. This applies to both prior and likelihood. *Quantile-based likelihood* is useful in models with sampling distributions which lack an explicit probability density function. *Quantile-based prior* allows for flexible distributions to express expert knowledge. The principle of *quantile-based* Bayesian inference is demonstrated in the univariate setting with a Govindarajulu likelihood, as well as in a *parametric quantile regression*, where the error term is described by a quantile function of a Flattened Skew-Logistic distribution.

Suggested Citation

  • Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "The tenets of quantile-based inference in Bayesian models," OSF Preprints enzgs_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:enzgs_v1
    DOI: 10.31219/osf.io/enzgs_v1
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    References listed on IDEAS

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    1. Perepolkin, Dmytro & Lindsröm, Erik & Sahlin, Ullrika, 2023. "Quantile-parameterized distributions for expert knowledge elicitation," OSF Preprints tq3an_v1, Center for Open Science.

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