In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies.

In the development of simplex mixed-effects models, random effects in these mixed-effects models are generally distributed in normal distribution. The normality assumption may be violated in an analysis of skewed and multimodal longitudinal data. In this paper, we adopt the centered Dirichlet process mixture model (CDPMM) to specify the random effects in the simplex mixed-effects models. Combining the block Gibbs sampler and the Metropolis–Hastings algorithm, we extend a Bayesian Lasso (BLasso) to simultaneously estimate unknown parameters of interest and select important covariates with nonzero effects in semiparametric simplex mixed-effects models. Several simulation studies and a real example are employed to illustrate the proposed methodologies.

The main purpose of this article is to develop a Bayesian adaptive lasso procedure for analyzing linear regression models with nonignorable missing responses, in which the missingness mechanism is specified by a logistic regression model. A sampling procedure combining the Gibbs sampler and Metropolis-Hastings algorithm is employed to obtain the Bayesian estimates of the regression coefficients, shrinkage coefficients, missingness mechanism models parameters, and their standard errors. We extend the partial posterior predictive p value for goodness-of-fit statistic to investigate the plausibility of the posited model. Finally, several simulation studies and the air pollution data example are undertaken to demonstrate the newly developed methodologies.

基于改进的Cholesky分解,研究分析了纵向数据下半参数联合均值协方差模型的贝叶斯估计和贝叶斯统计诊断,其中非参数部分采用B样条逼近.主要通过应用Gibbs抽样和Metropolis-Hastings算法相结合的混合算法获得模型中未知参数的贝叶斯估计和贝叶斯数据删除影响诊断统计量.并利用诊断统计量的大小来识别数据的异常点.模拟研究和实例分析都表明提出的贝叶斯估计和诊断方法是可行有效的.

本文研究泊松逆高斯回归模型的贝叶斯统计推断.基于应用Gibbs抽样,Metropolis-Hastings算法以及Multiple-Try Metropolis算法等MCMC统计方法计算模型未知参数和潜变量的联合贝叶斯估计,并引入两个拟合优度统计量来评价提出的泊松逆高斯回归模型的合理性.若干模拟研究与一个实证分析说明方法的可行性.

Logistic mixed-effects models are widely used to study the relationship between the binary response and covariates for longitudinal data analysis, where the random effects are typically assumed to have a fully parametric distribution. As this assumption is likely limited or unreasonable in a multitude of practical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of binomial distribution logistic mixed-effects models, a general Bayesian framework is presented in which a semiparametric hierarchical modelling with an approximate truncated Dirichlet process prior distribution is specified for the random effects. The stick-breaking prior and the blocked Gibbs sampler using Pólya-Gamma mixture are employed to efficiently sample in the posterior analysis. Besides, a procedure calculating DIC for Bayesian model comparison is addressed. The methodology is demonstrated through simulation studies and a real example.

罗尔中值定理是微积分解题需要用到的基本定理之一，是研究函数及其导函数关系的重要工具。本文首先对罗尔中值定理进行论述，然后通过例题对其应具体应用进行分析，重点阐述应用罗尔中值定理构造辅助函数的一般方法，使学生能够掌握罗尔中值定理在微积分解题中的使用技巧。

对响应变量带有不可忽略缺失数据的联合均值与方差模型的贝叶斯估计问题进行了研究.缺失数据机制通过logistic回归模型来指定,模型参数和缺失数据机制参数的联合贝叶斯估计通过运用MH算法及Gibbs抽样获得,并用数值计算阐明上述方法的可行性.

文章在非线性均值方差模型框架下基于K-L距离研究贝叶斯数据删除影响的统计诊断问题,通过应用Gibbs抽样和MH算法估计贝叶斯数据删除影响诊断统计量.随机模拟研究和红鳟鲑鱼数据的数值例子说明该诊断方法的可行性.

声波的散射问题中,如果散射体由不可穿透障碍物和可穿透裂缝两部分组成,障碍物表面分别满足第一类和第三类边界条件,裂缝两边满足不同的第二类边界条件,通过位势理论,可以将此混合问题转化为边界积分方程,通过Fredholm算子理论可以得到这个边界积分方程解的存在性和唯一性,从而获得原问题解的存在和唯一性.

受Kuo和Mallick思想的启发,文章应用Gibbs抽样和MH算法对联合均值与方差模型的贝叶斯变量选择问题进行研究.数值例子说明了该变量选择方法的可行性和有效性.

文章对逆高斯回归模型进行贝叶斯统计分析,通过利用Gibbs抽样和MH算法得到模型参数的贝叶斯估计以及贝叶斯数据删除诊断统计量的计算.数值模拟说明了方法的可行性.

本文主要研究三门问题,首先利用全概率公式计算得出其理论结果;其次,根据蒙特卡罗方法模拟得到其近似值,对比发现该近似方法非常有效.

讨论响应变量带有不可忽略缺失数据的非线性均值方差模型的Bayes估计问题.缺失数据机制由logistic回归模型来指定,运用Gibbs抽样及MH算法得到模型参数和缺失数据机制参数的联合Bayes估计,模拟研究和实例分析展示上述模型和方法的可行性.

Inspired by the idea of Kuo and Mallick, Bayesian subset selection for inverse Gauss regression models is studied by Gibbs sampler and Metropolis-Hastings algorithm in this paper. Simulation study and the aerobic fitness data example are employed to demonstrate the proposed methodology.

Bayesian analysis for joint mean and variance models is studied in this paper, in which Gibbs sampler and Metropolis-Hastings algorithm are used to calculate Bayesian estimations of unknown parameters and Bayesian case deletion diagnostic. Simulation studies and a real example are used to illustrate the proposed methodology.

声波的散射问题中,散射体由两部分组成:里面是一个不可穿透的障碍物,外面是一条可穿透的裂缝.不可穿透障碍物由两部分组成,不同部分的边界条件不同.通过位势理论可以将此混合问题转化为边界积分方程.通过Fredholm算子理论可以得到这个边界积分方程解的存在性和唯一性,从而获得原问题解的存在性和唯一性.

Simplex regression model is often employed to analyze continuous proportion data in many studies. In this paper, we extend the assumption of a constant dispersion parameter (homogeneity) to varying dispersion parameter (heterogeneity) in Simplex regression model, and present the B-spline to approximate the smoothing unknown function within the Bayesian framework. A hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is presented for sampling observations from the posterior distribution. The procedures for computing model comparison criteria such as conditional predictive ordinate statistic, deviance information criterion, and averaged mean squared error are presented. Also, we develop a computationally feasible Bayesian case-deletion influence measure based on the Kullback-Leibler divergence. Several simulation studies and a real example are employed to illustrate the proposed methodologies.

受Kuo和Mallick思想的启发,文章应用Gibbs抽样和MH算法研究单纯形分布联合位置与散度模型的贝叶斯变量选择问题.模拟研究的数值例子说明了该方法的可行性与有效性.