Nonparametric Bayes Estimation of Contamination Levels Using Observations from the Residual Distribution
利用阈值以上样本非参数贝叶斯估计污染水平AI 解读 ↓
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利用阈值以上样本非参数贝叶斯估计污染水平
- 研究问题
- 如何结合一般污染浓度测量与来自高浓度热点的阈值以上样本，估计污染分布及平均浓度，并处理删失和截断？
- 方法与思路
- 作者以 Dirichlet 过程表达污染分布的先验信息，构造非参数贝叶斯分布估计，允许一般测量右删失及热点样本左截断。
- 材料陈述的贡献
- 摘要称平均浓度的贝叶斯估计在多种成本函数下通常优于所比较方法，并说明非信息先验情形与非参数极大似然估计的联系。
- 阅读关注点
- 应核对热点抽样与一般样本的关系、删失和截断机制、先验极限的定义，以及与 Kaplan–Meier 估计一致的具体区间。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要解读。摘要未列出成本函数、比较设定或稳健性结果；“残余分布”指阈值以上分布，不能据此解释为回归残差。
原文摘要
Data on contamination concentrations for chromium from one of the EPA's toxic waste sites consist of independent and identically distributed (iid) measurements along with additional observations from the residual distribution. The residual sample is obtained by sampling from hot spots, where contamination concentrations are assumed to be above a given threshold value. The data are modeled using a nonparametric Bayes estimator of the distribution function. The Dirichlet process is used to formulate prior information about the chromium contamination, and we compare the Bayes estimator of the mean concentration level to other estimators currently considered by the EPA and other sources. The Bayes estimator of the mean generally outperforms competing estimators under various cost functions. The Bayes estimator of the distribution function is derived assuming the possibility of right-censored contamination measurements along with left-truncated hot spot data. For the case in which the prior becomes noninformative, the Bayes estimator of the distribution function is the nonparametric maximum likelihood estimator, which is identical to the Kaplan-Meier estimator for concentration values observed below the residual sample threshold. Robustness of the Bayes estimator is examined with respect to misspecification of the prior and its sensitivity to the censoring distribution.