关于序贯检验的Bayes分析

本文将充分利用验前信息的Ｂａｙｅｓ方法与序贯检验相结合,推导出了Ｂａｙｅｓ序贯检验方法。文章从表面形式上的决策方案推导到实质上真正的决策方案;并对飞行器落点密集度进行了模拟计算的具体分析,最后得出结论,Ｂａｙｅｓ序贯检验方法对具有昂贵成本的产品试验和我国航天试验有较大的应用价值．     

完全随机缺失数据下配对试验的Bayes分析

采用Bayes分析方法,对完全随机缺失下配对试验设计数据进行统计分析,给出了参数的Bayes后验概率密度函数及参数的置信区间计算表达式,并对基于Bayes分析的假设检验功效进行了模拟.从模拟结果看,Bayes分析检验功效一致性地高于缺失数据配对删除的t检验方法,特别,在缺失数据相对较多或配对数据相关系数较低时,其表现出更大优势.     

微子样假设检验在火箭工程中的应用

火箭落点偏差,是指火箭的实际落点与瞄准点的距离,它是一个随机变量,通常服从正态分布N(μ,σ~2),按其统计特征量分为火箭落点密集度(随机落点偏离散布中心的密集程度为偶然误差)和火箭落点精度(散布中心偏离瞄准点的程度为系统误差),经国家批准的《火箭研制任务书》均明确规定火箭落点密集度具体指标(通常给定标准差(σ)或概率偏差(E)的值),要通过飞行试验,检验标准差或概率偏差是否达到了国家给定的指标,而对火箭落点精度(μ)在《火箭研制任务书》中不作规定,因为此项误差按要求应当为零(实际上要通过试验、数据处     

导弹落点精度的一种Bayes估计方法

针对传统的区间估计法在导弹落点精度评定中不能完全反映实际情况的问题,本文在充分利用了各阶段试验信息的条件下提出了采用一种Bayes估计方法对导弹落点精度进行评定,并通过一组试验数据对该方法进行验证,结果表明本文所采用的方法比传统的区间估计法评定的导弹落点精度要高。     

线性回归模型的Bayes统计推断

Bayes方法虽融合了样本信息和先验信息，但利用的先验信息都是有历史经验和专家估计所得，因此可靠度不高。该文研究了正态线性回归模型：Y=Xβ＋e，e—N（0，σ^2。L），其中σ^2已知，β为未知参数向量，对传统的Bayes方法进行了改进，即把Bayes方法中的后验信息作为改进Bayes的无验信息并融合样本信息进行统计推断，在二次损失函数下得到了β的改进的Bayes估计。由于改进的Bayes方法的先验信息中有样本信息，因此其准确度比传统的Bayes方法准确度更高。     

产品失效率的验前分布稳健性分析

研究Bayes统计分析中利用验前信息的稳健性.首先,用一般方法研究了指数寿命型分布中失效率的验前分布的稳健性.然后利用Gamma分布函数的典型性质,并以平方损失下的后验期望损失为判别准则,讨论了失效率的最优Bayes稳健区间.给出了失效率的最优Bayes稳健点估计.     

正态分布在不同先验下的Bayes估计及风险比较

本文讨论在均值未知,方差已知的正态分布情况下通过在共轭先验以及Jeffreys先验二种先验下的Bayes估计问题,在平方损失函数下和线性损失函数下Bayes风险的比较.数据计算可以看出,在Jeffreys先验下的Bayes风险要比在共轭先验下的Bayes风险要大,但是当样本量增大时,两者的后验风险越来越靠近.     

双参数指数分布环境因子的Bayes估计

讨论了定数截尾样本下双参数指数分布环境因子的极大似然估计、区间估计和Bayes估计.以参数后验密度的商密度作为环境因子的后验密度,并结合专家经验运用Bayes方法给出了环境因子在平方损失下和LINEX损失下的Bayes估计.最后运用Monte Carlo方法对各估计结果的均方误差(MSE),进行了模拟比较.结果表明LINEX损失下环境因子的估计较好.     

稳健Bayes估计

在Bayes估计问题中,我们证明了当损失函数满足一定条件时,所对应的Bayes估计是稳健的:即Bayes估计是后验分布的连续泛函(相对于后验分布之间的Kolmogorov距离)。     

基于Jeffreys验前的Bayes方差估计修正

分析了基于Jeffreys验前的经典Bayes方差估计以及考虑验前信息可信度情况下Bayes方差估计存在的问题,在一般情况下,其方差估计要大于验前子样和验后子样的方差,这显然是不合理的.这是采用Jeffreys验前和正态共轭分布假设时存在的固有问题.为了解决这一问题,提出了方差估计的修正公式,经过计算验证,其值在验前子样和验后子样方差之间,说明修正公式是合理的.     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

Bases of the identities of products of certain varieties of groups

The following theorem is proved: The product of any variety of two-step solvable groups and a variety having a finite basis of identity relations has a finite basis of identity relations.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 137–144, January, 1969.