Bayesian prior robustness using general ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-divergence measureBayesian prior robustness using general...L. Harrouche et al.

被引：0

作者：

Lyasmine Harrouche ^{[1
]}

Hocine Fellag ^{[1
]}

Lynda Atil ^{[1
]}

机构：

[1] Mouloud Mammeri University,Laboratory of Pure and Applied Mathematics, Department of Mathematics

来源：

Statistical Papers | 2025年 / 66卷 / 1期

关键词：

Bayesian robustness; Classes of priors; Local curvature; Robustness measure; -divergence measure;

D O I：

10.1007/s00362-024-01628-z

中图分类号：

学科分类号：

摘要：

Bayesian robustness measure of classes of contaminated priors using general ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-divergence between two posterior distributions is introduced. Using the local curvature for the ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-divergence of the posterior distributions, we propose to extend the result of Dey and Birmiwal (1994), which consider the ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-contaminated and geometric mixing classes, to any prior contamination classes. Then, a new general explicit analytic formula for the local curvature is obtained. Moreover, we show that this curvature formula doesn’t depend on the contaminated posterior distribution and gives unified answers irrespective of the choice of the ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document} functions. As applications, both parametric and nonparametric prior contamination are considered.

引用