统计与数据科学学院知识库

在大数据和人工智能的时代背景下，小样本的统计估计问题仍是需要攻克的 难题，而地震中人员死亡数的评估同样是小样本问题，因此，论文旨在利用经验 贝叶斯方法，构建基于扩大样本数据的经验贝叶斯估计方法，并以1950-2022年 中国大陆地区历史震例数据进行该方法的研究，以期望科学评估地震造成的人员 死亡损失并为地震应急救援决策部署提供新的理论方法与科学依据。

首先，论文对地震人员死亡从时间分布、空间分布及对影响地震人员死亡因 素方面进行分析，对主要影响因素极震区烈度、发震时间及人口密度进行分析， 并基于这三个主要影响因素建立三级归类场景。

其次，构建Bootstrap-EB 的小样本估计方法，采用Bootstrap重抽样法对各 场景下地震人员死亡数据进行扩充，并对扩充后的虚拟数据进行质量评估；再将 扩充后的数据进行极大似然估计将其估计结果作为先验分布，采用贝叶斯公式给 出不同场景下地震人员死亡变化分布函数；进而根据实际情况对后验分布进行截 断分析，以明确地震人员死亡的不确定性变化范围及死亡率区间概率值。

最后，对Bootstrap-EB 方法进行评估，针对该方法所估算的地震人员死亡率 及死亡人数进行点估计和区间估计结果进行评估，具体地，随机选取历史震例检 验该结果的精度及交叉验证该评估方法的稳定性；再将该方法与贝叶斯方法、极 大似然估计方法以及业内模型进行对比；结果表明该方法的估计效果较高，并与 实际情况较为相符，为地震灾区紧急救援工作提供支持，帮助合理分配抗震救援 和医疗人员，提供决策依据。

In the era of big data and artificial intelligence, the problem of statistical estimation of small samples is still a problem to be solved, and the estimation of death toll in earthquakes is also a problem of small samples, the purpose of this paper is to construct a Empirical Bayes method method based on expanded sample data using empirical Bayes method, and to study this method using historical earthquake case data of Chinese mainland area from 1950 to 2022, it is expected to scientifically evaluate the loss of life caused by earthquake and provide new theoretical methods and scientific basis for earthquake emergency rescue decision-making.

First of all, the paper analyzes the death of earthquake personnel from the time distribution, the spatial distribution and the factors affecting the death of earthquake personnel, and analyzes the main factors, such as the intensity of the extreme earthquake area, the time of earthquake occurrence and the population density, and based on these three main factors to establish a three-level classification scenario.

Secondly, Bootstrap-eb method is constructed to estimate small samples, and Bootstrap resampling method is used to expand the death data of seismic personnel in each scene, and the quality of the expanded virtual data is evaluated Then, the expanded data were maximum likelihood and the estimated results were taken as a prior distribution, and the distribution functions of death were given by Bayesian formula under different scenarios Then, the posterior distribution is truncated according to the actual situation, in order to make clear the uncertain range of death and the interval probability value of death rate.

Finally, the Bootstrap-EB method is evaluated, and the results of point estimation and interval estimation are evaluated according to the estimated death rate and death number of earthquake personnel, the accuracy of the method is tested by randomly selected historical earthquake cases and the stability of the method is verified by cross-validation, then the method is compared with the EB method, the maximum likelihood method and the industry model Finally, the error of this method is analyzed, and the result shows that this method has a good estimation effect, and it accords with the actual situation, it can widely provide decision support and basis for post-earthquake emergency rescue, reasonable distribution of earthquake rescue and medical personnel.