Bayesian Inference Of Semi-parametric Skew-normal Spatial Autoregression Models

Spatial correlation often exists between different data of the same variable due to the interaction of geographical locations.The Spatial Autoregressive Models adequately consider the spatial correlation of spatial data.In real life,not all spatial data follow strictly normal distribution because the data often have skewed characteristics.The independent variables have not only linear but also partially nonlinear effects on the response variables.The traditional spatial autoregressive model cannot consider the skewed characteristics of spatial data and the nonlinear effects of the independent variables.If these effects are neglected,it is easy to cause inadequate use of data information,resulting in large bias or even wrong estimation.The skew-normal distribution introduces skewness into the normal distribution,which can better handle multi-peaked and thick-tailed data at the same time and with the excellent characteristics of normal distribution.The semiparametric model can effectively tap the linear and nonlinear features of the data.Based on the excellent properties of Skewnormal distribution and non-parametric models,this thesis proposes a Semi-parametric Skew-normal Spatial Autoregressive Model and systematically investigates its Bayesian statistical inference.The specific work carried out in this thesis is as follows:(1)Bayesian inference of the Semiparametric Skew-normal Spatial Autoregressive Model is investigated.Firstly,a Semiparametric Skew-normal Spatial Autoregressive Model is established under the assumption that the random error terms obey a skew-normal distribution.Secondly,the nonparametric part of the model is approximated by using Bayesian P-samples.Finally,the posterior distribution samples are extracted using MCMC algorithm to obtain the Bayesian estimates of the model parameters.In addition,the effectiveness of the model approach is illustrated by simulation studies and example analysis.(2)Bayesian inference of the Semiparametric Skew-normal Spatial Autoregressive Model based on the Dirichlet process is investigated.First,the variance is assumed to obey a class of unknown nonparametric distributions,a flexible family of distributions(Dirichlet process)is used to model the variance,and P splines are used to approximate the nonparametric part of the model.Second,the MCMC algorithm is used to achieve Bayesian parameter estimation.Finally,the feasibility of the model approach is illustrated by simulations and example studies.(3)Bayesian inference of a Semiparametric Skew-normal Spatial Autoregressive Model with non-negligible missing is studied.First,the presence of non-negligible missing data in the dependent variable is considered,and the missing data mechanism is specified by the logistic regression model.Secondly,the Bayesian parameter estimation of the model is implemented using MCMC algorithm.Finally,the rationality of the model approach is demonstrated by simulations and examples.