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The tenets of quantile-based inference in Bayesian models

Perepolkin, Dmytro LU orcid ; Goodrich, Benjamin and Sahlin, Ullrika LU orcid (2023) In Computational Statistics and Data Analysis 187.
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.

Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bayesian analysis, Parametric quantile regression, Quantile functions, Quantile-based inference
in
Computational Statistics and Data Analysis
volume
187
article number
107795
pages
15 pages
publisher
Elsevier
external identifiers
  • scopus:85162099398
ISSN
0167-9473
DOI
10.1016/j.csda.2023.107795
language
English
LU publication?
yes
id
ae7bfd65-2f17-4bd6-8e85-6ee952934cf0
date added to LUP
2023-08-23 15:17:06
date last changed
2025-10-14 09:30:22
@article{ae7bfd65-2f17-4bd6-8e85-6ee952934cf0,
  abstract     = {{<p>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.</p>}},
  author       = {{Perepolkin, Dmytro and Goodrich, Benjamin and Sahlin, Ullrika}},
  issn         = {{0167-9473}},
  keywords     = {{Bayesian analysis; Parametric quantile regression; Quantile functions; Quantile-based inference}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Computational Statistics and Data Analysis}},
  title        = {{The tenets of quantile-based inference in Bayesian models}},
  url          = {{http://dx.doi.org/10.1016/j.csda.2023.107795}},
  doi          = {{10.1016/j.csda.2023.107795}},
  volume       = {{187}},
  year         = {{2023}},
}