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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2810 |
| _version_ | 1827678078372937728 |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:56:35Z |
| format | Article |
| id | doaj.art-2d6daa1138754818bd80002dcb145d25 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:56:35Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2d6daa1138754818bd80002dcb145d252023-11-22T21:19:11ZengMDPI AGMathematics2227-73902021-11-01921281010.3390/math9212810Bayesian Inference under Small Sample Sizes Using General Noninformative PriorsJingjing He0Wei Wang1Min Huang2Shaohua Wang3Xuefei Guan4School of Reliability and Systems Engineering, Beihang University, Beijing 100191, ChinaSchool of Reliability and Systems Engineering, Beihang University, Beijing 100191, ChinaSchool of Reliability and Systems Engineering, Beihang University, Beijing 100191, ChinaChina Aviation Power Plant Research Institute, Zhuzhou 412002, ChinaGraduate School of China Academy of Engineering Physics, Beijing 100193, ChinaThis 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.https://www.mdpi.com/2227-7390/9/21/2810Bayesian inferencenoninformative priorJeffreys’ priorinvariant |
| spellingShingle | Jingjing He Wei Wang Min Huang Shaohua Wang Xuefei Guan Bayesian Inference under Small Sample Sizes Using General Noninformative Priors Mathematics Bayesian inference noninformative prior Jeffreys’ prior invariant |
| title | 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_short | Bayesian Inference under Small Sample Sizes Using General Noninformative Priors |
| title_sort | bayesian inference under small sample sizes using general noninformative priors |
| topic | Bayesian inference noninformative prior Jeffreys’ prior invariant |
| url | https://www.mdpi.com/2227-7390/9/21/2810 |
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