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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, 2023. "The tenets of quantile-based inference in Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:csdana:v:187:y:2023:i:c:s0167947323001068
    DOI: 10.1016/j.csda.2023.107795
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