基于Pair-copula的贝叶斯空间预测模型及其在雾霾监测中的应用

发布时间：2018-07-03 01:37

本文选题：Pair-copula结构 + 空间相依结构　；参考：《重庆工商大学》2017年硕士论文

【摘要】：随着研究问题的复杂化和全面化,空间统计分析技术目前已成为理论研究的热点,其主要原因是该方法融入了研究主体的空间信息,较好地反映出了空间因素的影响作用,因此,它被广泛应用到经济、水文等领域。空间数据结构的日益丰富使描述空间依赖性关系变得愈加复杂,如何利用空间数据构造空间联合分布模型并准确估计参数以达到空间插值预测的目的仍是一大难点。空间数据分析中,大多数研究文献仍是利用变差函数描述观测变量的空间相依结构、利用Kriging插值法或其派生出的多种方法进行空间预测。Bárdossy(2006)指出,这两种方法对异常值比较敏感且易受到边缘分布的影响,并首次利用Copula函数描述空间数据的空间相关结构。Copula函数本质上是边缘分布函数对联合分布的映射,它能够将相关结构和边缘分布这两种信息“隔离”,在有效克服上述问题基础上也为构造联合分布提供了一种有效的方法。考虑到两两变量间不一定服从同一分布的情况,本文利用Pair-copula结构将不同的边缘分布函数连接起来,避免了传统多元Copula函数一致性的限制,使所建模型更加灵活和多元化,能更好地反映多变量之间的相关关系。另外,对模型中参数的估计问题,通常采用极大似然估计(MLE)法,即把参数看做一个确定的数值,所得估计结果为点估计,无法反映多变量间的相依关系和结构,同时,在高维数据或参数过多情况下计算繁杂,即使使用数值方法也会在计算方面花费过多时间。因此,本文利用贝叶斯估计法,它能够充分利用样本信息和参数的先验信息,在对模型参数进行估计时,通常贝叶斯估计量能够得到更小的方差或平方误差,不仅可以构造较高精度的置信区间,而且具有稳健性。本文将空间Pair-copula模型及其参数估计纳入到一个完整的理论框架中,着力于利用Pair-copula函数结合研究变量的空间位置信息和空间相关性构建多变量联合分布,通过贝叶斯估计法得到有效的参数估计值,利用交叉验证法将空间Pair-copula模型的预测结果与传统Kriging插值方法的结果进行对比验证模型具有更高的预测精度,最后结合重庆市主城区雾霾监测站的PM2.5浓度数据对研究区域中任意位置的数据进行空间插值预测。
[Abstract]:With the complexity and comprehensiveness of the research problem, the spatial statistical analysis technology has become the focus of theoretical research at present. The main reason is that the method integrates the spatial information of the main body of the research, which reflects the influence of the spatial factors. Therefore, it is widely used in economic, hydrological and other fields. With the increasing enrichment of spatial data structure, it becomes more and more complicated to describe the spatial dependence relationship. How to use spatial data to construct spatial joint distribution model and estimate parameters accurately to achieve the purpose of spatial interpolation prediction is still a big difficulty. In spatial data analysis, most research papers still use variation function to describe the spatial dependent structure of observation variables. Kriging interpolation method or its derived methods are used for spatial prediction. B 谩 rdossy (2006) points out, These two methods are sensitive to outliers and vulnerable to the influence of edge distribution. Copula function is used to describe spatial correlation structure of spatial data for the first time. Copula function is essentially the mapping of edge distribution function to joint distribution. It can "isolate" the two kinds of information such as the correlation structure and the edge distribution. It also provides an effective method for constructing the joint distribution on the basis of overcoming the above problems effectively. Considering the fact that the two variables do not necessarily follow the same distribution, this paper uses the Pair-copula structure to connect the different edge distribution functions, which avoids the limitation of the consistency of the traditional multivariate Copula functions and makes the model more flexible and diversified. It can better reflect the correlation between multivariable. In addition, the maximum likelihood estimation (MLE) method is usually used to estimate the parameters in the model, that is to say, the parameters are regarded as a definite value. The estimated results are point estimation, which can not reflect the dependence and structure of the multivariable, and at the same time, the maximum likelihood estimation (MLE) method is used to estimate the parameters of the model. In the case of high dimensional data or too many parameters, even the use of numerical methods will take too much time to calculate. Therefore, this paper uses Bayesian estimation method, which can make full use of the sample information and the prior information of the parameters. In the estimation of model parameters, usually Bayesian estimators can get smaller variance or square error. Not only the confidence interval with high accuracy can be constructed, but also the confidence interval is robust. In this paper, the spatial Pair-copula model and its parameter estimation are incorporated into a complete theoretical framework, and the multi-variable joint distribution is constructed by combining the Pair-copula function with the spatial location information and spatial correlation of variables. The effective parameter estimates are obtained by Bayesian estimation method. The prediction results of spatial Pair-copula model are compared with those of the traditional Kriging interpolation method, and the prediction accuracy of the model is higher than that of the traditional Kriging interpolation method. Finally, based on the PM2.5 concentration data of haze monitoring station in Chongqing main urban area, the data of any position in the study area are predicted by spatial interpolation.
【学位授予单位】：重庆工商大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：X513

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