论文标题
小样本量下的贝叶斯推断 - 一种非信息的先验方法
Bayesian inference under small sample size -- A noninformative prior approach
论文作者
论文摘要
本文提出了针对小样本和稀疏数据问题的贝叶斯推论方法。提出了一种一般类型的先验类型（$ \ propto 1/σ^{q} $），以制定贝叶斯后部针对小样本量下的推理问题。结果表明，这种类型的先验可以代表广泛的先验，例如经典的非信息先验和渐近的局部不变先验。在这项研究中进一步表明，此类先验可以得出作为正常内伽马偶联先验的限制状态，从而可以对贝叶斯后期和预测因子进行分析评估。使用全局可能性比较了不同样本量下不同非信息先验的性能。拉普拉斯近似方法用于评估全局可能性。数值线性回归问题和现实的疲劳可靠性问题用于演示该方法并确定最佳的非信息性先验。结果表明使用Jeffreys的先前表现其他其他人的预测变量。显示了非信息性贝叶斯估计量比在较小样本量下的常规最小平方估计器的优点。
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/σ^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small sample size. It is shown that this type of prior can represents a broad range of priors such as classical noninformative priors and asymptotically locally invariant priors. It is further shown in this study that such priors 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 size is compared using the global likelihood. The method of Laplace approximation is employed to evaluate the global likelihood. A numerical linear regression problem and a realistic fatigue reliability problem are used to demonstrate the method and identify the optimal noninformative prior. Results indicate the predictor using Jeffreys' prior outperforms others. The advantage of the noninformative Bayesian estimator over the regular least square estimator under small sample size is shown.
