Spatial Factor Copula Model Based On Bayesian Estimation And Application In Temperature Analysis

As one of the important meteorological data,temperature plays an important role in various aspects of social life,but due to the real conditions such as geographical location and financial resources,it is impossible to establish a large and reasonable number of meteorological stations in every province and city.Since temperature data has rich spatial characteristics information,how to use the appropriate spatial joint distribution function to describe the temperature variation,choose an efficient and simple method to estimate its parameters,and choose a suitable method to interpolate the temperature prediction is the focus of this paper.The literature that takes temperature as the research object economically establishes a correlation model based on the historical temperature of a region,and spatially interpolates and predicts the regional temperature by interpolation methods,which will ignore the linkage of temperature changes in neighboring regions and the dependence of temperature on the tails.In this paper,we choose a spatial factorial Copula model to analyze temperature variables with spatial characteristics,and reflect the spatial dependence of variables with distance by a power exponential covariance function,which not only enriches the study object of Copula function,but also takes into account the historical temperature changes in neighboring regions and the dependence of temperatures on tails.In the parameter estimation,the literature uses great likelihood to estimate the parameters of the spatial factor Copula model,this paper combines the prior information,sample information,and this paper innovatively uses the MH algorithm in MCMC method to estimate the parameters in the spatial factor Copula model,which reduces the difficulty of parameter estimation.According to the estimation results,it can be seen that the dynamic iterative trajectory graph of each parameter is smooth;in the cross-validation,it is verified that the spatial interpolation effect based on the spatial factor Copula model is better than the three traditional spatial interpolation methods of IDW,OK and UK,and the mean square error of the former is smaller.The empirical analysis was conducted with the temperature of meteorological stations in nine areas in the center of the main metropolitan area of Chongqing,and the calculation of the upper and lower tail coefficients revealed that the parameter estimates controlling the dependent structure of the upper tail were larger than those controlling the dependent structure of the lower tail,and the temperature changes were more dependent at the lower tail than the upper tail,while the parameter values estimated by the MH algorithm were consistent with the actual situation,i.e.,the number of temperature drops or sudden temperature drops and frequency is higher than that of the warming state.The spatial interpolation prediction can be carried out for any area according to different geographical location information.From the prediction results,it is found that the interpolation effect is better for the first 10 days,and the obtained temperature prediction data are consistent with the actual temperature values,indicating that the spatial interpolation prediction results are stable,and the temperature values of the districts and counties near the Yangtze River basin are always higher than those of other districts and counties.