The Parameter Estimation And Application Of Spatially Varying Coefficient Autoregressive Models With Bayesian

Due to the rapid development of modern society, the amount of spatial data being in the exponential explosion growth. However, because spatial data has special properties, such as spatial autocorrelation and spatial heterogeneity(also known as non-stationary space) compared with general attribute data. Therefore, the model of spatial data must choose a data integration which is different from the general mathematical model of a special nature, in order to better represent the spatial patterns and spatial relationships.The introduction of the article, a comprehensive overview of the two mathematical models which were used in different research areas for the special properties of the spatial data. Spatial Autoregressive models(SAR) and Spatially Varying Coefficient processes(SVCP), which describes the current situation of the two models,the attention of scholars and the widely applied in different ?elds.In this paper, the geographic space of spatial data has been added into the Spatial Autoregressive models, thus the regression coefficient of original Spatial Autoregressive models has changed into a regression coefficient function which relats geographic data, so forming the Spatially Varying Coefficient Autoregressive models(SVCAM).This model is different from the SAR and the SVCP, which is widely used.The new model consider both the spatial autocorrelation and the spatial heterogeneity of spatial data,which in the form of geographic data.Therefore, the results of SVCAM not only describe the relationship between the independent variables and the dependent variable, but also re?ect the spatial variation of data.This analysis comes from the environment, the economy, urban management and planning, geography, and other ?elds have a wide application of spatial data.To further research of different ?eld spatial data presented more advanced research methods.In addition, for the estimation of the parameters β(u, v), ρ, σ2of the model, we use the geographically weighted regression(GWR) gives the estimated ofβ(u, v), ρ, σ2. As for the parameters ρ,Bayesian approach is chosen prior distribution parameters considered, given the ρ of the posterior distribution.In the empirical analysis in this paper, based on the daily temperature and precipitation data at 53 representative meteorological stations in Xinjiang during1970,1980,1990 and 2000, using the Spatially Varying Coefficient Autoregressive models analysis the spatial heterogeneitythe of the regression relationship between average temperature and annual precipitation of Xinjiang region, and the results be visualized. The results not only illustrate the temperature and precipitation in the Xinjiang region have signi?cant effects space aggregation, also showed that there are obvious regional differences among the in?uences of temperature on precipitation inXinjiangregion.