半参数贝叶斯空间建模方法在地震灾害数据中的应用

发布时间：2018-05-15 08:00

本文选题：k-ZIG + 狄利克雷混合过程先验　；参考：《昆明理工大学》2017年硕士论文

【摘要】：我国是世界上多地震的国家,也是蒙受地震灾害最为严重的国家之一.中国地处世界上两个最大地震集中发生地带——环太平洋地震带与欧亚地震带之间,受太平洋板块、印度板块和菲律宾海板块的挤压.中国地震活动频度高、强度大、震源浅,分布广,是一个震灾严重的国家.20世纪有1/3的陆上破坏性地震发生在我国,死亡人数约60万,占全世界同期因地震死亡人数的一半左右.因此本文以1974年至2006年全国21个省份的地震灾害数据为研究对象,分析地震灾害的地理变化趋势和区域异质性.本文第二章主要讨论了死亡人数与震级、经度、纬度和地震发生地区之间的关系.通过分析我们发现死亡人数具有明显的零点膨胀特征,因此选择k-ZIG模型拟合地震灾害数据.k-ZIG的回归模型部分主要由三部分组成,其一是线性部分,主要用于刻画固定效应.其二为关于经纬度的二维光滑曲面,这一部分主要用于解释大的空间趋势.本文采用结合惩罚样条的"Box乘积"以及二阶随机游走先验的建模方法,这在很大程度上降低了数据维数,避免了经纬度数据处理过程中常见的"维数灾难"问题.其三为空间随机效应,这一部分则主要反映了小范围内的区域异质性.对空间随机效应考虑狄利克雷混合过程先验,在此基础上绘制出地震高发地区的"Disease Mapping"地图,动态呈现高的相对风险区域随时空变化的趋势.本文第三章主要讨论了震级与死亡人数、经度、纬度和地震发生地区之间的关系.实际中,我们通常会重点关注地震等级大于一定级别的地震,而对于微小等级的地震(即危害程度很小的地震),我们并不太关心.因此,考虑贝叶斯特定分位数下的回归是有实际意义的.为克服非对称拉普拉斯分布的局限性,在本文重点考虑灵活分位数回归.灵活分位数回归的基本思想是两个正态分布的无限混合.在这部分的回归模型与第二章回归模型部分相同,在本章对空间随机效应考虑高斯条件自回归结构.本文通过结合近年来计数数据、贝叶斯分位数回归和统计计算方面的新思路新成果,较为系统地研究了基于k-ZIG的半参数空间随机效应模型和基于灵活分位数回归的半参数空间随机效应模型.通过监测不同时期的"Disease Mapping"地图的变化情况,动态地把握地震灾害的发展变化趋势,这对于我国的灾害风险评估是极具意义的.通过分析可以证明本文方法的有效性和可行性.本文将当代统计学中热点问题的自然结合和推广,适应了实际问题中对复杂数据分析的需要,是一项有价值的探索,在研究内容上有所创新,统计推断方法上也更有特色.此外,本文模型也将考虑结合更复杂的结构或时间相关性进行研究.
[Abstract]:China is a country with many earthquakes in the world, and also one of the countries that suffer the most serious earthquake disaster. China is located between the Pacific Rim seismic belt and the Eurasian seismic belt, which is squeezed by the Pacific plate, the Indian plate and the Philippine Sea plate. China has a high frequency of seismicity, a large intensity, a shallow earthquake source and a wide distribution. It is a country with severe earthquake disasters. In the 20th century, a third of the destructive earthquakes on land occurred in China, with a death toll of about 600000. It accounts for about half of the world's earthquake deaths in the same period. Therefore, based on the seismic disaster data of 21 provinces from 1974 to 2006, this paper analyzes the trend of geographical change and regional heterogeneity of earthquake disasters. In the second chapter, the relationship between the number of dead and magnitude, longitude, latitude and earthquake occurrence area is discussed. We find that the number of dead has the characteristic of zero expansion, so the regression model of fitting seismic disaster data .k-ZIG with k-ZIG model is composed of three parts, one is linear part, which is mainly used to describe the fixed effect. The second is a two-dimensional smooth surface about latitude and longitude, which is mainly used to explain the large spatial trend. In this paper, the method of "Box product" combined with penalty spline and a second-order random walk priori are used to reduce the data dimension to a great extent and to avoid the problem of "dimension disaster" in the process of processing longitude and latitude data. The third is spatial random effect, which mainly reflects the regional heterogeneity in a small range. Considering the Delikley mixing process for spatial random effects, the "Disease Mapping" map of seismic high risk area is drawn on the basis of which the dynamic trend of high relative risk region is presented. The third chapter mainly discusses the relationship between magnitude and the number of dead, longitude, latitude and earthquake occurrence area. In practice, we usually focus on earthquakes with a magnitude greater than a certain magnitude, but we don't care much about small ones (that is, small ones). Therefore, it is of practical significance to consider the regression under Bayesian specific quantiles. In order to overcome the limitation of asymmetric Laplace distribution, flexible quantile regression is considered in this paper. The basic idea of flexible quantile regression is the infinite mixing of two normal distributions. The regression model in this part is the same as that in the second chapter. In this chapter, the Gao Si conditional autoregressive structure is considered for spatial random effects. In this paper, new ideas and achievements in Bayesian quartile regression and statistical calculation are obtained by combining the counting data in recent years. The semi-parametric spatial random effect model based on k-ZIG and the semi-parametric spatial random effect model based on flexible quantile regression are studied systematically. By monitoring the change of "Disease Mapping" map in different periods, we can dynamically grasp the development trend of earthquake disaster, which is of great significance for disaster risk assessment in China. The effectiveness and feasibility of this method can be proved by analysis. This paper combines and generalizes the hot issues in contemporary statistics to meet the needs of complex data analysis in practical problems. It is a valuable exploration with some innovations in research contents and more distinctive statistical inference methods. In addition, the model will also consider a more complex structure or time correlation for the study.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P315.9;O212.8

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