Bayesian analysis of non-linear structural equation models with non-ignorable missing outcomes from reproductive dispersion models

Non-linear structural equation models are widely used to analyze the relationships among outcomes and latent variables in modern educational, medical, social and psychological studies. However, the existing theories and methods for analyzing non-linear structural equation models focus on the assumptions of outcomes from an exponential family, and hence can’t be used to analyze non-exponential family outcomes. In this paper, a Bayesian method is developed to analyze non-linear structural equation models in which the manifest variables are from a reproductive dispersion model (RDM) and/or may be missing with non-ignorable missingness mechanism. The non-ignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings algorithm is used to obtain the joint Bayesian estimates of structural parameters, latent variables and parameters in the logistic regression model, and a procedure calculating the Bayes factor for model comparison is given via path sampling. A goodness-of-fit statistic is proposed to assess the plausibility of the posited model. A simulation study and a real example are presented to illustrate the newly developed Bayesian methodologies.     

Integral modular data and congruences

We compute all fusion algebras with symmetric rational S-matrix up to dimension 12. Only two of them may be used as S-matrices in a modular datum: the S-matrices of the quantum doubles of ℤ/2ℤ and S ₃. Almost all of them satisfy a certain congruence which has some interesting implications, for example for their degrees. We also give explicitly an infinite sequence of modular data with rational S- and T-matrices which are neither tensor products of smaller modular data nor S-matrices of quantum doubles of finite groups. For some sequences of finite groups (certain subdirect products of S ₃,D ₄,Q ₈,S ₄), we prove the rationality of the S-matrices of their quantum doubles.     

核实数据下响应变量缺失的线性EV模型经验似然推断

考虑响应变量随机缺失而协变量带有误差的线性模型,借助于核实数据和借补方法,构造了回归系数的两种经验似然比,证明了所提出的估计的经验对数似然比渐近于一个自由度为1的独立χ2变量的加权和;而经调整后所得的调整经验对数似然比渐近于自由度为p的χ2分布,该结果可以用来构造未知参数的置信域.此外,我们也构造了响应均值的调整经验对数似然比统计量,并证明了所提出的统计量渐近于x2分布,可用此结果构造响应均值的置信域.通过模拟研究比较了置信域的精度及其平均区间长度.     

存在不精确数据情况下的环境效率分析

针对环境效率评价问题中存在不精确数据的一类典型问题进行了深入的分析,在回顾现有的不精确数据处理方法以及环境效率评价方法的基础上,基于加性DEA模型,提出一种新的环境效率评价方法.该方法不仅能够求解各个投入/产出数据的最佳精确值,而且能够进一步分析各个决策单元的无效性.通过算例分析对模型及方法的优越性进行了说明,提出的方法克服了现有不精确数据处理方法的局限性,能够有效地处理环境效率分析问题中的不精确数据,得到更为准确的环境管理信息,为环境管理提供更为有效的决策依据.     

基于性能退化的动量轮可靠性建模与评估

为解决长寿命卫星动量轮可靠性评估无失效数据问题,研究基于性能退化的动量轮可靠性建模与评估方法.首先通过失效分析,提出以温度作为动量轮可靠性的特征量.然后利用动量轮温度的遥测数据,建立其温度随时间变化的叠合模型.为解决动量轮试验样本量不足问题,采用Bootstrap仿真方法建立动量轮寿命分布模型,评估其可靠性水平.实例表明,方法能够在无失效数据情况下,利用性能退化数据评估动量轮可靠性,且具有较高精度,为解决无失效数据条件下长寿命卫星动量轮可靠性建模与评估问题提供了一条有效途径.     

纵向数据边际模型非参数光滑方法的比较

对于纵向数据边际模型的均值函数, 有很多非参数估计方法, 其中回归样条, 光滑样条, 似乎不相关(SUR)核估计等方法在工作协方差阵正确指定时具有最小的渐近方差. 回归样条的渐近偏差与工作协方差阵无关, 而SUR核估计和光滑样条估计的渐近偏差却依赖于工作协方差阵. 本文主要研究了回归样条, 光滑样条和SUR核估计的效率问题. 通过模拟比较发现回归样条估计的表现比较稳定, 在大多数情况下比光滑样条估计和SUR核估计的效率高.     

Box-Cox变换用于分位数回归曲线相交问题的研究

将Box-Cox变换与分位数回归模型相结合(两阶段法),是分位数回归研究领域的一大进步。该法虽然两步都与分位数回归的检验函数紧密结合,但是由于没有利用分位数回归的优良性质,而是引入了中间参变量,因此增加了模型的累进误差,降低了模型精度。更重要的是,两阶段法没有对于分位数回归领域中普遍出现的分位数回归曲线的相交问题给出解决方法。针对这些问题,经研究应该首先确定Box-Cox变换的参数,避免模型中不确定因素的引入,然后对数据进行整体变换并结合分位数检验函数,直接利用分位数回归的优良性质,最终确定分位数回归模型的参数。实例证明,该方法提高了模型的精度,可以有效地解决分位数回归曲线的相交问题。     

On the k-sample Behrens-Fisher problem for high-dimensional data

For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s T ² test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however, the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the classical Hotelling’s T ² test not powerful or not even well defined. To overcome this difficulty, we propose and study an L ²-norm based test. The asymptotic powers of the proposed L ²-norm based test and Hotelling’s T ² test are derived and theoretically compared. Methods for implementing the L ²-norm based test are described. Simulation studies are conducted to compare the L ²-norm based test and Hotelling’s T ² test when the latter can be well defined, and to compare the proposed implementation methods for the L ²-norm based test otherwise. The methodologies are motivated and illustrated by a real data example. The work was supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112)     

A selective view of stochastic inference and modeling problems in nanoscale biophysics

Advances in nanotechnology enable scientists for the first time to study biological processes on a nanoscale molecule-by-molecule basis. They also raise challenges and opportunities for statisticians and applied probabilists. To exemplify the stochastic inference and modeling problems in the field, this paper discusses a few selected cases, ranging from likelihood inference, Bayesian data augmentation, and semi- and non-parametric inference of nanometric biochemical systems to the utilization of stochastic integro-differential equations and stochastic networks to model single-molecule biophysical processes. We discuss the statistical and probabilistic issues as well as the biophysical motivation and physical meaning behind the problems, emphasizing the analysis and modeling of real experimental data. This work was supported by the United States National Science Fundation Career Award (Grant No. DMS-0449204)     

利用远场模式的不完全数据反演声波阻尼系数

从阻尼边界条件声波散射问题的散射场远场模式的部分数据信息出发给出了反演声波阻尼系数的一种新方法,该问题既是非线性的又是不适定的,这里利用Tikhonov正则化方法将问题转化为一个最优化问题,成功地处理了第一类算子方程的不适定性及该问题的非线性性,给出了具体的数值方法并对其收敛性进行了严格地证明,数值结果表明该方法是非常准确且简单易行的．