有序响应变量的贝叶斯模型选择及其在COPD疾病防治中的应用

慢性阻塞性肺病(COPD)是一种发病率、死亡率都非常高的疾病,且COPD的诊断和严重程度分级依赖于肺功能的检查,但是由于肺功能检查仪器价格昂贵,使得这项检查在很多经济欠发达地区尤其是农村基层医院并没有普及。本文基于有序响应变量模型致力于研究一种便于基层和社区使用的可以初步判别COPD病情的模型,以期提高我国基层和社区的COPD 防治水平。利用贝叶斯变量选择方法和数据增强的潜变量策略得到了易于实施的Gibbs后验抽样算法。数值模拟分析进一步说明了本文提出的有序响应变量贝叶斯模型选择方法的有效性,实例分析得到了易于判别COPD严重程度的稀疏模型。     

半连续Bernoulli-Normal两部回归模型及变量选择

对于半连续两部回归模型,考虑到每个回归部分都会遇到大量的候选变量,此时就会产生变量选择问题。文章主要研究Bernoulli-Normal两部回归模型的变量选择问题。先提出一种基于Lasso惩罚函数的变量选择方法,但考虑到Lasso估计量不具有Oracle性质,又提出一种基于自适应Lasso惩罚函数的变量选择方法。模拟结果表明：两种方法都能够对Bernoulli-Normal回归模型进行变量选择,且自适应Lasso方法的变量选择性能往往优于Lasso方法。     

Cox模型中的自适应Lasso变量选择

文章考虑了Cox模型的变量选择问题,将自适应Lasso引入到Cox模型中,提出了一类基于惩罚偏似然函数的自适应Lasso估计程序.通过对偏似然函数采用二阶泰勒展开式近似逼近,运用循环坐标下降法求解模型,再借助牛顿-拉普森迭代完成整个变量选择和估计过程.随机数据模拟的结果表明该方法具有优良的变量选择效果,并适用于高维数据.     

大样本线性回归模型的子抽样及变量选择

文章考虑了大样本下线性回归中同时进行快速估计和变量选择的问题,即针对一个存在稀疏解的大样本线性模型,根据重要性抽样分布从全数据集抽取少量子样本,对该子样本进行自适应Lasso估计。通过随机模拟研究,将该算法分别应用在几种不同的数据集中,并从模型预测精度和可解释性两个方面比较了四种子抽样方法在该算法下的表现。模拟结果表明,所提出的算法具有良好表现,在计算开销上也具有一定优势。     

中国经济增长的决定因素分析——基于贝叶斯模型平均（BMA）方法的实证研究

采用贝叶斯模型平均（Bayesian Model Averaging）方法,使用1990-2007年省际数据,对长期影响中国经济增长的诸多因素的有效性和稳健性进行了识别和检验。研究结论表明：高等教育发展阶段、工业化推进速度、对外开放程度、东部区位优势、消费能力和对内开放水平等6个解释变量对中国经济增长具有长期、持续和稳健的影响,是中国经济增长的长期决定因素。城市规模、中部区位优势和初始经济条件等3个解释变量对经济增长也具有一定的解释能力。此外,从解释变量对经济增长边际影响的程度来看,工业化推进速度变量对经济增长的边际影响最强,其次是消费能力变量和对外开放程度变量。     

大数据背景下贝叶斯模型平均的理论突破与应用前景

大数据统计分析过程中常面临模型比较和选择的不确定性问题。贝叶斯模型平均(BMA)方法可以通过先验和后验概率度量模型不确定性,并利用后验概率对模型的结果进行加权平均,最终得到更稳健的估计结果。在回顾贝叶斯模型平均发展历程的基础上,介绍贝叶斯模型平均的基本原理,综述其在一些难点问题上的理论进展,并介绍大数据背景下贝叶斯模型平均的应用前景。贝叶斯模型平均与复杂数据分析方法相结合,可能成为大数据研究的新思路。     

基于贝叶斯模型平均方法的影响SHIBOR定价因素的实证

上海银行间同业拆放利率(SHIBOR)作为我国货币市场基准利率,研究影响SHIBOR定价因素有重要意义。文章提出利用贝叶斯模型平均方法来选择影响SHIBOR定价因素,使用随机搜索变量选择方法来有效的对模型集合中模型进行抽签。研究结果表明:一年期人民币银行贷款利率、回购利率、上一日SHIBOR报价和资金成本对上海同业拆借市场利率存在长期的正的影响,是影响SHIBOR定价的决定因素。     

贝叶斯分位数回归组间组内变量选择及其应用

文章利用贝叶斯方法研究分位数回归的组间和组内双变量选择问题。基于偏态拉普拉斯分布和贝叶斯统计推断方法,结合组间和组内系数的Spike-and-Slab先验分布,提出了分位数回归的贝叶斯双层变量选择方法,并给出易于实施的Gibbs后验抽样算法。通过大量数值模拟和实证分析验证了所提变量选择方法的有效性。     

变量选择偏离对预测的影响研究

模型选择目的可以分为两类:一类是变量选择,另一类是预测分析.文章系统地研究了两种目的异同和建模时要注意的问题,提出了变量选择偏离的概念及其与预测的关系.     

带有有序变量的结构方程模型中的模型选择

文章着重研究了带有有序分类变量的结构方程模型的模型选择问题,并将一个基于贝叶斯准则的统计量称为测度,应用到此类模型中进行模型选择。通过实例分析说明了上述方法的应用,并给出了根据贝叶斯因子进行模型选择的结果。     

Two-Stage Bayesian Model Averaging in Endogenous Variable Models

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50% in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed.     

Bayesian Model Selection and Averaging in Additive and Proportional Hazards Models

Although Cox proportional hazards regression is the default analysis for time to event data, there is typically uncertainty about whether the effects of a predictor are more appropriately characterized by a multiplicative or additive model. To accommodate this uncertainty, we place a model selection prior on the coefficients in an additive-multiplicative hazards model. This prior assigns positive probability, not only to the model that has both additive and multiplicative effects for each predictor, but also to sub-models corresponding to no association, to only additive effects, and to only proportional effects. The additive component of the model is constrained to ensure non-negative hazards, a condition often violated by current methods. After augmenting the data with Poisson latent variables, the prior is conditionally conjugate, and posterior computation can proceed via an efficient Gibbs sampling algorithm. Simulation study results are presented, and the methodology is illustrated using data from the Framingham heart study.     

Bayesian Variable Selection Under Collinearity

In this article, we highlight some interesting facts about Bayesian variable selection methods for linear regression models in settings where the design matrix exhibits strong collinearity. We first demonstrate via real data analysis and simulation studies that summaries of the posterior distribution based on marginal and joint distributions may give conflicting results for assessing the importance of strongly correlated covariates. The natural question is which one should be used in practice. The simulation studies suggest that posterior inclusion probabilities and Bayes factors that evaluate the importance of correlated covariates jointly are more appropriate, and some priors may be more adversely affected in such a setting. To obtain a better understanding behind the phenomenon, we study some toy examples with Zellner’s g-prior. The results show that strong collinearity may lead to a multimodal posterior distribution over models, in which joint summaries are more appropriate than marginal summaries. Thus, we recommend a routine examination of the correlation matrix and calculation of the joint inclusion probabilities for correlated covariates, in addition to marginal inclusion probabilities, for assessing the importance of covariates in Bayesian variable selection.     

Bayesian Variable Selection in Markov Mixture Models

Monte Carlo simulation is used to evaluate the actual confidence levels of five different approximations for confidence intervals for the probability of success in Markov dependent trials. The approximations involve the conditional probability of success as a nuisance parameter, and the effects of substituting Klotz's (1973), Price's (1976), and a new estimator are also evaluated. The new estimator is less biased and tends to increase the confidence level. A program for calculating the estimator and the confidence interval approximations is available.     

非正态分布下具有自回归误差项的空间自回归模型变量选择研究

将变量选择引入空间计量模型,讨论具有自回归误差项的空间自回归模型的变量选择问题。在残差非正态独立同分布的条件下,通过最大化信息熵,提出空间信息准则,并证明其在该模型变量选择中具有一致性。模拟研究结果表明:无论对单个系数还是对全部系数,空间信息准则都能很好识别,且与经典的赤池准则相比具有较大的优势。因此,空间信息准则是一种更为有效的变量选择方法。     

Logistic回归的双层变量选择研究

变量选择是统计建模的重要环节,选择合适的变量可以建立结构简单、预测精准的稳健模型。本文在logistic回归下提出了新的双层变量选择惩罚方法——adaptive Sparse Group Lasso(adSGL),其独特之处在于基于变量的分组结构作筛选,实现了组内和组间双层选择。该方法的优点是对各单个系数和组系数采取不同程度的惩罚,避免了过度惩罚大系数,从而提高了模型的估计和预测精度。求解的难点是惩罚似然函数不是严格凸的,因此本文基于组坐标下降法求解模型,并建立了调整参数的选取准则。模拟分析表明,对比现有代表性方法Sparse Group Lasso、Group Lasso及Lasso,adSGL法不仅提高了双层选择精度,而且降低了模型误差。最后本文将adSGL法应用到信用卡信用评分研究,对比logistic回归,它具有更高的分类精度和稳健性。     

Focused Information Criteria,Model Selection,and Model Averaging in a Tobit Model With a Nonzero Threshold

Claeskens and Hjort (2003 Claeskens, G. and Hjort, N. L. 2003. “The Focused Information Criterion”. Journal of the American Statistical Association, 98: 900–945. (with discussion)[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) have developed a focused information criterion (FIC) for model selection that selects different models based on different focused functions with those functions tailored to the parameters singled out for interest. Hjort and Claeskens (2003 Hjort, N. L. and Claeskens, G. 2003. “Frequentist Model Average Estimators”. Journal of the American Statistical Association, 98: 879–899. (with discussion)[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) also have presented model averaging as an alternative to model selection, and suggested a local misspecification framework for studying the limiting distributions and asymptotic risk properties of post-model selection and model average estimators in parametric models. Despite the burgeoning literature on Tobit models, little work has been done on model selection explicitly in the Tobit context. In this article we propose FICs for variable selection allowing for such measures as mean absolute deviation, mean squared error, and expected expected linear exponential errors in a type I Tobit model with an unknown threshold. We also develop a model average Tobit estimator using values of a smoothed version of the FIC as weights. We study the finite-sample performance of model selection and model average estimators resulting from various FICs via a Monte Carlo experiment, and demonstrate the possibility of using a model screening procedure before combining the models. Finally, we present an example from a well-known study on married women's working hours to illustrate the estimation methods discussed. This article has supplementary material online.     

基于TVP-VAR模型的自适应Lasso惩罚变量选择方法

文章将自适应Lasso变量选择方法扩展到变系数向量自回归模型(TVP-VAR)中.利用所提出方法对2005-2014年航空煤油价格与民航货邮与旅客周转量月度数据进行分析,并与其他四种方法进行了比较,结果显示:与常系数VAR模型相比,变系数VAR模型能够显著提高模型的拟合与预测精度.提出的自适应Lasso变系数模型一致优于Belmonte,Koop和Korobolis(2014)提出的Lasso变系数模型.