Semiparametric Bayesian Spatial Modeling Method With An Application To Earthquake Disaster Data

Earthquake disaster is one of the most serious natural disasters.China is located in the circum Pacific seismic belt and the Eurasian seismic belt,and is also one of the countries suffering from earthquake disaster.In the 20th century,one-third of the land-borne devastating earthquake occurred in China,the death toll was about 600,000,accounting for about half of the world's death toll from the earthquake.Therefore,this paper takes the earthquake disaster data of 21 provinces in China from 1974 to 2006 as the research object,and analyzes the geographical change trend and regional heterogeneity of earthquake disaster.In the second chapter,we mainly discuss the relationship between the number of deaths and the magnitude,longitude,latitude and earthquake occurrence area.Through the analysis we find that the death number has obvious zero expansion characteristics,so we choose the k-ZIG model to fit the earthquake disaster data.The regression model of k-ZIG is mainly composed of three parts,one is the linear part,mainly used to describe the fixed effect.The second is about the two-dimensional smooth surface of latitude and longitude,this part is mainly used to explain the large spatial trend.In this paper,.we use the "Box product" combined with the penalized spline and the second-order random walk a priori modeling method,which greatly reduces the data dimension and avoids the "dimension disaster" common in latitude and longitude data processing.The third is the spatial random effect,which mainly reflects the regional heterogeneity.In this part,we consider the Dirichlet Process Mixture prior.On this basis,we draw the "Disease Mapping" map of the earthquake prone area,and dynamically show the high relative risk area with the trend of time and space changes.In the third chapter of this paper,we mainly discuss the relationship between magnitude and death,longitude,latitude and earthquake occurrence.In practice,we usually focus on earthquakes with magnitude greater than a certain level,and we do not care much about tiny earthquakes.Therefore,it is of practical significance to consider Bayesian quantile regression.In order to overcome the limitation of the asymmetric Laplace distribution,we focus on the flexible quantile regression.The basic idea of flexible quantile regression is the infinite mixing of two normal distributions.In this part,the regression model is the same as the second chapter.In this chapter,we consider the Gauss autoregressive structure.Based on the new results of counting data,Bayesian quantile regression and statistical calculation in recent years,this paper systematically studied the semi-parametric spatial random effect model based on k-ZIG and flexible bayesian quantile regression for semiparametric geoadditve mixed models.By monitoring the changes of the "Disease Mapping" map in different periods,we can dynamically grasp the development trend of earthquake disaster,which is very meaningful for disaster risk assessment in China.The validity and feasibility of the proposed method are proved by analysis.In this paper,the combination and popularization of hot issues in contemporary statistics is adapted to the need of complex data analysis in practical problems.It is a valuable exploration,innovation in the research content and more in the method of statistical inference.In addition,the model will also be considered in conjunction with more complex structures or temporal correlations.