Spatial Bayesian Modeling And Its Application In Seismic Data Of Mainland China

Because of its relative professional background knowledge and strong application background,spatial statistics has always been one of the hot topics in statistics research.The spatial geological data is characterized by complex structure,many potential influence factors,large information content,and high computational requirements.For a long time,the related researches are mostly confined to the relatively simple epidemiological studies of the theoretical methods,species distribution studies and disease mortality distribution studies,are rarely involved in seismic data with extremely valuable application.China is located at the intersection of the world's two major seismic belts,the Pacific Rim Earthquake Belt and the Eurasian Earthquake Belt.It is squeezed by the Pacific Plate,the Indian Plate,and the Philippine Sea Plate.The seismic fault zone is very active.The tectonic position of the Earth is determined,and earthquakes frequently occur seriously.China's earthquakes are mainly distributed in five regions: Southwest China,Northwest China,North China,Southeast China,and 23 seismic belts.In the 20 th century,there were 3 earthquakes with magnitude 8.6 or more in the world,including two it occurred in China;the 1976 Tangshan earthquake in Hebei province caused more than 240,000 deaths.It is also unique in the world.China has a high frequency of earthquake activity,a large intensity,a shallow source,and a wide distribution.It is a country with a severe earthquake disaster.The severity of earthquakes and other natural disasters constitutes one of China's basic national conditions.Statistics show that China's land area accounts for global Onefifth of the land area;China's population accounts for about one-fifth of the world's population.However,China's terrestrial earthquakes account for one-third of the global terrestrial earthquakes,and the number of earthquake deaths has reached 1/2 of the global population.The reason for this is that in addition to the fact that China has a large population density and relatively backward economy,it is also closely related to the strong and frequent features of seismic activity in China.Therefore,this paper intends to establish a spatial Bayesian statistical inference program for the above data using the seismic data of mainland China.Overall,the work of this paper can be roughly divided into two parts.The first part focuses on Bayesian space.Nonparametric models are used for the application of hybrid response variables and seismic data in China.In the second part,Bayesian Copula spatial geological data modeling is studied.Specifically,in Chapter 2,the main considerations are response variables,confounding variables,and The variable uses the method of joint modeling.This model is based on a Gaussian conditional autoregressive(CAR)model,combining the species sampling model(SSM)and the probit truncated stick process prior to the data to solve the complex interactions.The key idea is to introduce spatial dependencies by modeling the weights of Gauss-Markov random fields or discrete random probability metrics of SSM.This chapter illustrates practicality and effectiveness the method through examples of seismic datasets in China.In chapter 3 of this paper,we mainly discuss the method based on spatial Bayesian Copula,and use the data adding technique combined with the MCMC method to establish a Bayesian Copula modeling method for binary random variables.Due to the complexity of the data,the following two cases are mainly discussed: the first case is a Bayesian Copula modeling method for binary discrete random variables;and the second is a Bayesian Copula modeling method for binary mixed random variables.As we all know,the advantage of the Bayesian modeling method is that it does not depend on the of the sample size,and it can obtain relatively ideal estimation results in the case of small samples,which is meaningful for the quantifiable catastrophe risk assessment extreme value theory with limited data volume.The Bayesian method is especially suitable for models with relatively complex structure levels and can simplify calculations to a certain extent.The non-parametric modeling of spatially geologic data's hybrid response variables used in this paper has been adapted to practical research.The need for disaster risk control combines the relatively popular new techniques of joint modeling in contemporary statistics,such as the Bayesian Copula modeling method,and presents a research program that is compatible with practical problems,which has a certain guidance significance for the prevention and control of catastrophic risks.