The tenets of quantile-based inference in Bayesian models

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 like-lihood. 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 demon-strated 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.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).