Bayesian Inference under Small Sample Sizes Using General Noninformative Priors

Jingjing He, Wei Wang, Min Huang, Shaohua Wang and Xuefei Guan
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Jingjing He: School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Wei Wang: School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Min Huang: School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Shaohua Wang: China Aviation Power Plant Research Institute, Zhuzhou 412002, China
Xuefei Guan: Graduate School of China Academy of Engineering Physics, Beijing 100193, China

Mathematics, 2021, vol. 9, issue 21, 1-20

Abstract: 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.

Keywords: Bayesian inference; noninformative prior; Jeffreys’ prior; invariant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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