Weibull分布下基于MCMC的贝叶斯恒加试验数据评估

本文基于贝叶斯生存分析理论,在参数的有信息先验假设条件下,通过运用基于Gibbs抽样的马尔可夫链蒙特卡罗(MCMC)方法动态模拟出相关参数后验分布的马尔可夫链,给出恒加试验模型中各参数的贝叶斯估计;利用BUGS软件包对文献[6]中的实例进行建模分析,并将两种假设条件下MCMC具有显著差异的计算结果与传统BLUE结果进行比较,发现BLUE的计算结果近似等于将产品截尾数据当作失效数据时MCMC的处理结果;进而再次揭示出传统BLUE方法的不足,并证明了该模型在可靠性应用中的直观性与有效性。     

基于MCMC模拟的贝叶斯 AR-GJR-GARCH 模型及其应用

AR-GJR-GARCH模型是一种误差项为GJR-GARCH形式的自回归模型,该模型的贝叶斯推断很难得到其具体形式的条件后验密度。文章利用Metropolis-Hastings抽样方法对模型参数的条件后验分布进行MCMC模拟,然后运用模拟得到的样本对模型的参数进行贝叶斯估计。该方法解决了参数估计过程中的高维数值积分问题。模拟结果表明了该模型在中国股市波动性分析过程中的直观性和有效性。     

真实固定效应空间随机前沿模型的贝叶斯估计

忽略个体效应和空间效应会严重干扰效率测算,其中忽略个体效应使得技术无效率项发生偏移,忽略空间相关性导致估计量有偏且不一致。本文基于真实固定效应随机前沿模型（引入了个体效应）,引入因变量和双边误差项的空间滞后项,构建了适用性更佳的真实固定效应空间随机前沿模型。对模型进行组内变化以消除额外参数,使用贝叶斯方法（需推导未知参数的后验分布并执行MCMC抽样）估计参数和技术效率。该方法真正克服了额外参数问题,比同类方法直观、简便。数值模拟结果表明,本文方法对参数、个体截距项及技术无效率项的估计精度均较高,且增加样本容量,估计精度变优。     

行政记录整合的贝叶斯分层记录链接模型及应用

记录链接的技术问题与统计理论密切相关,尤其是在建立记录链接分类规则时需要构建统计模型,识别关键变量以完成数据匹配。在贝叶斯框架下构建分层模型整合行政记录,通过多元回归可以实现匹配错误率的估计,而且一对一限制下的记录链接允许通过模块反映记录信息的来源变化,基于MCMC模拟的后验分布计算方便,有助于提高数据整合效率。     

基于MCMC和贝叶斯的AR（1）-MA（0）双重模型的参数估计

为了解决AR（1）-MA（0）双重模型的参数估计问题,文章引入一种新的方法即基于MCMC和贝叶斯估计方法,对该模型的参数进行了估计,系统地推导出了模型中各参数的估计值;通过数值模拟,说明用该方法估计此类模型的参数是可行的,且与传统方法相比更易于实现。     

半参数空间ZISF的估计及反馈分类

本文引入空间效应、非参函数和非连续分布技术无效率项,构建了半参数空间0无效率随机前沿模型(简称为半参数空间ZISF),模型的适用性更广,可有效避免函数形式误设和忽略内生性问题导致的有偏和不一致估计量.对非参函数采用B样条逼近,使用极大似然方法和JLMS法可得到参数(含非参数函数)和技术效率的估计.基于伯努利大数定律提出反馈分类,可将技术无效率项分类.蒙特卡罗模拟表明:①本文方法的估计精度较高.增加样本容量后,估计精度更优.忽略任意一种效应将导致估计精度降低.②分类阈值的跨度较大,主观判断贝叶斯后验概率的大小进而将技术无效率项分类的可靠性较低.反馈分类的准确率较高且必要.     

广义线性混合模型框架下的信度模型分析

尝试在广义线性混合模型的框架下构建信度模型。在广义线性混合模型框架中,假定被解释变量服从指数簇分布,假定自然参数先验分布为相应的自然共轭先验分布簇,按照Bayes理论,通过特殊构造,给出推论:对随机效应的估计满足经典信度公式。参数估计部分,利用自然共轭先验分布簇参数子列上下极限的性质找出先验分布参数的含义和关系,使用伪似然方法给出信度估计公式。并以特例形式讨论Tweedie模型,对模型进行变形,得到特例的Bühlmann-Straub信度和经典的Bühlmann信度。该模型同时考虑先验信息与后验信息,对整合分类费率与个体经验费率提供一定参考。     

基于贝叶斯搜索方法的TAR模型研究

文章基于贝叶斯随机搜索方法的思想,提出一种有效解决门限自回归(TAR)模型的贝叶斯方法,在不假设固定的机制个数条件下,借助拉丁变量建立贝叶斯随机搜索TAR模型.在此模型下,拉丁变量的后验分布包含了机制的个数和门限参数的信息,因此滞后阶数、门限值和所有回归系数等的估计均通过MCMC方法从其后验分布抽样.并从模型AR(1)、TAR(2,1,1)、TAR(3,1,1,1)中产生样本,模拟结果表明此方法能很好地估计机制数、延迟参数、门限值及各机制下的回归系数.用贝叶斯随机搜索TAR模型对太阳黑子年度数据集进行分析,找到三个门限值,即10.2,40和73,与已有文献中用其他方法得到的结果一致.     

稀有事件变点问题的Bayes分析

文章针对稀有事件中的变点问题,根据Bayes法建立了判断变点是否存在、计算变点位置的合理模型,并利用基于Gibbs抽样的MCMC模拟抽样,估计出变点和分布参数之值。然后引用美国煤矿灾难和我国关中地区干旱灾害的实际数据,对文中提出的模型进行验证,得出了有关结论。     

基于MCMC稳态模拟的异质性经济增长模型研究

 针对同质性增长模型无法描述各个经济体经济增长存在的异质性现象,提出了一类基于MCMC稳态模拟的异质性经济增长模型,它可以用来描述经济增长的异质性以及政策变量的差异影响。由于模型参数的后验条件分布没有确定的分布形式,通过数据扩充得到参数的完全条件分布从而实现模型参数的贝叶斯估计。对改革开放以来我国各省市区经济增长收敛性进行分析发现大规模股份制改革前经济增长具有同质性而大规模股份制改革后经济增长具有异质性,且可以用新古典经济增长理论来解释各地区经济的发展状况。     

Relabelling in Bayesian mixture models by pivotal units

Label switching is a well-known and fundamental problem in Bayesian estimation of finite mixture models. It arises when exploring complex posterior distributions by Markov Chain Monte Carlo (MCMC) algorithms, because the likelihood of the model is invariant to the relabelling of mixture components. If the MCMC sampler randomly switches labels, then it is unsuitable for exploring the posterior distributions for component-related parameters. In this paper, a new procedure based on the post-MCMC relabelling of the chains is proposed. The main idea of the method is to perform a clustering technique on the similarity matrix, obtained through the MCMC sample, whose elements are the probabilities that any two units in the observed sample are drawn from the same component. Although it cannot be generalized to any situation, it may be handy in many applications because of its simplicity and very low computational burden.     

Markov chain Monte Carlo methods for parameter estimation of the modified Weibull distribution

In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of a modified Weibull distribution based on a complete sample. While maximum-likelihood estimation (MLE) is the most used method for parameter estimation, MCMC has recently emerged as a good alternative. When applied to parameter estimation, MCMC methods have been shown to be easy to implement computationally, the estimates always exist and are statistically consistent, and their probability intervals are convenient to construct. Details of applying MCMC to parameter estimation for the modified Weibull model are elaborated and a numerical example is presented to illustrate the methods of inference discussed in this paper. To compare MCMC with MLE, a simulation study is provided, and the differences between the estimates obtained by the two algorithms are examined.     

Bayesian sequential inference for nonlinear multivariate diffusions

In this paper, we adapt recently developed simulation-based sequential algorithms to the problem concerning the Bayesian analysis of discretely observed diffusion processes. The estimation framework involves the introduction of m−1 latent data points between every pair of observations. Sequential MCMC methods are then used to sample the posterior distribution of the latent data and the model parameters on-line. The method is applied to the estimation of parameters in a simple stochastic volatility model (SV) of the U.S. short-term interest rate. We also provide a simulation study to validate our method, using synthetic data generated by the SV model with parameters calibrated to match weekly observations of the U.S. short-term interest rate.     

On the performance of the Bayesian composite likelihood estimation of max-stable processes

The max-stable process is a natural approach for modelling extrenal dependence in spatial data. However, the estimation is difficult due to the intractability of the full likelihoods. One approach that can be used to estimate the posterior distribution of the parameters of the max-stable process is to employ composite likelihoods in the Markov chain Monte Carlo (MCMC) samplers, possibly with adjustment of the credible intervals. In this paper, we investigate the performance of the composite likelihood-based MCMC samplers under various settings of the Gaussian extreme value process and the Brown–Resnick process. Based on our findings, some suggestions are made to facilitate the application of this estimator in real data.     

Bayesian composite quantile regression for linear mixed-effects models

Longitudinal data are commonly modeled with the normal mixed-effects models. Most modeling methods are based on traditional mean regression, which results in non robust estimation when suffering extreme values or outliers. Median regression is also not a best choice to estimation especially for non normal errors. Compared to conventional modeling methods, composite quantile regression can provide robust estimation results even for non normal errors. In this paper, based on a so-called pseudo composite asymmetric Laplace distribution (PCALD), we develop a Bayesian treatment to composite quantile regression for mixed-effects models. Furthermore, with the location-scale mixture representation of the PCALD, we establish a Bayesian hierarchical model and achieve the posterior inference of all unknown parameters and latent variables using Markov Chain Monte Carlo (MCMC) method. Finally, this newly developed procedure is illustrated by some Monte Carlo simulations and a case analysis of HIV/AIDS clinical data set.     

Bayesian Time Series Analysis of Structural Changes in Level and Trend

In this article we consider the problem of detecting changes in level and trend in time series model in which the number of change-points is unknown. The approach of Bayesian stochastic search model selection is introduced to detect the configuration of changes in a time series. The number and positions of change-points are determined by a sequence of change-dependent parameters. The sequence is estimated by its posterior distribution via the maximum a posteriori (MAP) estimation. Markov chain Monte Carlo (MCMC) method is used to estimate posterior distributions of parameters. Some actual data examples including a time series of traffic accidents and two hydrological time series are analyzed.     

Markov chain Monte Carlo estimation of a mixture item response theory model

Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods.     

Bayesian multiple comparison of models for binary data with inequality constraints

In this paper we consider generalized linear models for binary data subject to inequality constraints on the regression coefficients, and propose a simple and efficient Bayesian method for parameter estimation and model selection by using Markov chain Monte Carlo (MCMC). In implementing MCMC, we introduce appropriate latent variables and use a simple approximation of a link function, to resolve computational difficulties and obtain convenient forms for full conditional posterior densities of elements of parameters. Bayes factors are computed via the Savage-Dickey density ratios and the method of Oh (Comput. Stat. Data Anal. 29:411–427, 1999), for which posterior samples from the full model with no degenerate parameter and the full conditional posterior densities of elements are needed. Since it uses one set of posterior samples from the full model for any model in consideration, it performs simultaneous comparison of all possible models and is very efficient compared with other model selection methods which require one to fit all candidate models. A simulation study shows that significant improvements can be made by taking the constraints into account. Real data on purchase intention of a product subject to order constraints is analyzed by using the proposed method. The analysis results show that there exist some price changes which significantly affect the consumer behavior. The results also show the importance of simultaneous comparison of models rather than separate pairwise comparisons of models since the latter may yield misleading results from ignoring possible correlations between parameters.     

Bayesian Estimation of the Parameters of Bivariate Exponential Distributions

In this article, we develop an empirical Bayesian approach for the Bayesian estimation of parameters in four bivariate exponential (BVE) distributions. We have opted for gamma distribution as a prior for the parameters of the model in which the hyper parameters have been estimated based on the method of moments and maximum likelihood estimates (MLEs). A simulation study was conducted to compute empirical Bayesian estimates of the parameters and their standard errors. We use moment estimators or MLEs to estimate the hyper parameters of the prior distributions. Furthermore, we compare the posterior mode of parameters obtained by different prior distributions and the Bayesian estimates based on gamma priors are very close to the true values as compared to improper priors. We use MCMC method to obtain the posterior mean and compared the same using the improper priors and the classical estimates, MLEs.