Bayesian Inference under Small Sample Sizes Using General Noninformative Priors

This paper proposes a Bayesian inference method for problems with small sample sizes. A general type of noninformative prior is proposed to formulate the Bayesian posterior. It is shown that this type of prior can represent a broad range of priors such as classical noninformative priors and asymptot...

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Autores principales:	Jingjing He, Wei Wang, Min Huang, Shaohua Wang, Xuefei Guan
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Bayesian inference noninformative prior Jeffreys’ prior invariant Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2d6daa1138754818bd80002dcb145d25
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id	oai:doaj.org-article:2d6daa1138754818bd80002dcb145d25
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spelling	oai:doaj.org-article:2d6daa1138754818bd80002dcb145d252021-11-11T18:20:35ZBayesian Inference under Small Sample Sizes Using General Noninformative Priors10.3390/math92128102227-7390https://doaj.org/article/2d6daa1138754818bd80002dcb145d252021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2810https://doaj.org/toc/2227-7390This paper proposes a Bayesian inference method for problems with small sample sizes. A general type of noninformative prior is proposed to formulate the Bayesian posterior. It is shown that this type of prior can represent a broad range of priors such as classical noninformative priors and asymptotically locally invariant priors and can be derived as the limiting states of normal-inverse-Gamma conjugate priors, allowing for analytical evaluations of Bayesian posteriors and predictors. The performance of different noninformative priors under small sample sizes is compared using the likelihood combining both fitting and prediction performances. Laplace approximation is used to evaluate the likelihood. A realistic fatigue reliability problem was used to illustrate the method. Following that, an actual aeroengine disk lifing application with two test samples is presented, and the results are compared with the existing method.Jingjing HeWei WangMin HuangShaohua WangXuefei GuanMDPI AGarticleBayesian inferencenoninformative priorJeffreys’ priorinvariantMathematicsQA1-939ENMathematics, Vol 9, Iss 2810, p 2810 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bayesian inference noninformative prior Jeffreys’ prior invariant Mathematics QA1-939
spellingShingle	Bayesian inference noninformative prior Jeffreys’ prior invariant Mathematics QA1-939 Jingjing He Wei Wang Min Huang Shaohua Wang Xuefei Guan Bayesian Inference under Small Sample Sizes Using General Noninformative Priors
description	This paper proposes a Bayesian inference method for problems with small sample sizes. A general type of noninformative prior is proposed to formulate the Bayesian posterior. It is shown that this type of prior can represent a broad range of priors such as classical noninformative priors and asymptotically locally invariant priors and can be derived as the limiting states of normal-inverse-Gamma conjugate priors, allowing for analytical evaluations of Bayesian posteriors and predictors. The performance of different noninformative priors under small sample sizes is compared using the likelihood combining both fitting and prediction performances. Laplace approximation is used to evaluate the likelihood. A realistic fatigue reliability problem was used to illustrate the method. Following that, an actual aeroengine disk lifing application with two test samples is presented, and the results are compared with the existing method.
format	article
author	Jingjing He Wei Wang Min Huang Shaohua Wang Xuefei Guan
author_facet	Jingjing He Wei Wang Min Huang Shaohua Wang Xuefei Guan
author_sort	Jingjing He
title	Bayesian Inference under Small Sample Sizes Using General Noninformative Priors
title_short	Bayesian Inference under Small Sample Sizes Using General Noninformative Priors
title_full	Bayesian Inference under Small Sample Sizes Using General Noninformative Priors
title_fullStr	Bayesian Inference under Small Sample Sizes Using General Noninformative Priors
title_full_unstemmed	Bayesian Inference under Small Sample Sizes Using General Noninformative Priors
title_sort	bayesian inference under small sample sizes using general noninformative priors
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/2d6daa1138754818bd80002dcb145d25
work_keys_str_mv	AT jingjinghe bayesianinferenceundersmallsamplesizesusinggeneralnoninformativepriors AT weiwang bayesianinferenceundersmallsamplesizesusinggeneralnoninformativepriors AT minhuang bayesianinferenceundersmallsamplesizesusinggeneralnoninformativepriors AT shaohuawang bayesianinferenceundersmallsamplesizesusinggeneralnoninformativepriors AT xuefeiguan bayesianinferenceundersmallsamplesizesusinggeneralnoninformativepriors
_version_	1718431872822804480

Bayesian Inference under Small Sample Sizes Using General Noninformative Priors

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