Bayes Spatial Prediction Model Based On Pair-copula And Its Application In Haze Monitor

With the complication and comprehensiveness of research,spatial statistical analysis technology has become a hot topic in theoretical research.The main reason is that the method integrates the spatial information of research subject,which can better reflect the influence of spatial factors.Therefore,it is widely used in the field of economics,hydrology and so on.The increasing spatial data structure makes the description of spatial dependency more complicated.So,how to construct spatial joint distribution model with spatial data and accurately estimate the parameters in order to achieve the purpose of spatial interpolation prediction is still a difficult problem.In the spatial data analysis,most of the research literatures still use the variogram to describe the spatial dependent structure of the observed variables,and use the Kriging interpolation method or its various derived methods to practice the prediction.Bárdossy(2006)pointed out that these two methods are more sensitive to the outliers and are susceptible to marginal distribution,and for the first time used the Copula function to describe the spatial correlation of spatial data.The Copula function is essentially a mapping of the edge distribution function to the joint distribution,which can "isolate" two kinds of information about dependency structure and marginal distribution,and provide an effective method for constructing joint distribution on the basis of effectively overcoming the above problems.Considering that the two variables are not necessarily subject to the same distribution,this paper uses the Pair-copula structure to connect the different marginal distribution functions,which avoids the limitation of the consistency of the traditional multi-copula function,makes the model more flexible and diversified,and can better reflect the relationship between multiple variables.In addition,the estimation of parameters in the model is usually based on the maximum likelihood estimation(MLE)method,that is,the parameters as a certain value,the estimated results for the point estimation,which can not reflect theinterdependence between the dependencies and structure.At the same time,in the case of high-dimensional data or too many parameters of the calculation,even if the use of numerical methods will spend too much time in the calculation.Therefore,this paper uses the Bayesian estimation method,which can make full use of the prior information of the sample information and parameters.When the model parameters are estimated,the Bayesian estimator can obtain smaller variance or square error,and a higher confidence interval and a robustness.In this paper,the spatial Pair-copula model and its parameter estimation are incorporated into a complete theoretical framework.The Pair-copula function is used to construct the multivariate joint distribution based on the spatial location information and spatial correlation of the variables.The Bayesian estimation method The results of the Pair-copula model are compared with the results of the traditional Kriging interpolation method to verify that the model has higher prediction accuracy.Finally,combined with the PM2.5 of the main city haze monitoring station in Chongqing,the concentration data is used to interpolate the data at any position in the study area.