低渗气藏非线形方程新模型的适定性

研究了低渗透气藏中气体滑脱效应问题,利用气体滑脱现象对气测渗透率的影响,建立了低渗透多孔介质气体渗流规律的非线性抛物型偏微分方程、非线性边界条件的数学模型,论证了其适定性,得到了该模型解的存在、唯一及稳定的理论证明,为数值计算奠定了基础。     

Alternative Bayes factors for model selection

Several alternative Bayes factors have been recently proposed in order to solve the problem of the extreme sensitivity of the Bayes factor to the priors of models under comparison. Specifically, the impossibility of using the Bayes factor with standard noninformative priors for model comparison has led to the introduction of new automatic criteria, such as the posterior Bayes factor (Aitkin 1991), the intrinsic Bayes factors (Berger and Pericchi 1996b) and the fractional Bayes factor (O'Hagan 1995). We derive some interesting properties of the fractional Bayes factor that provide justifications for its use additional to the ones given by O'Hagan. We further argue that the use of the fractional Bayes factor, originally introduced to cope with improper priors, is also useful in a robust analysis. Finally, using usual classes of priors, we compare several alternative Bayes factors for the problem of testing the point null hypothesis in the univariate normal model.     

计算水溶液中电解质相对偏摩尔焓的新模型

以德拜－休克尔公式计算的活度系数为基础，由计算机曲线拟合，给出了水溶液中电解质相对偏摩尔焓的计算通式．     

On an improved Erdő-Rényi-type law for increments of partial sums

Let X₁, X₂,… be an independently and identically distributed sequence with ξX₁ = 0, ξ exp (tX₁ < ∞ (t ≧ 0) and partial sums S_n = X₁ + … + X_n. Consider the maximum increment D₁ (N, K) = max_{0≤n ≤ N - K} (S_{n + K} - S_n)of the sequence (S_n) in (0, N) over a time K = K_N, 1 ≦ K ≦ N. Under appropriate conditions on (K_N) it is shown that in the case K_N/log N → 0, but K_N/(log N)^1/2 → ∞, there exists a sequence (α_N) such that K_-1/2 D₁ (N, K) - α_N converges to 0 w. p. 1. This result provides a small increment analogue to the improved Erd?s-Rényi-type laws stated by Csörg? and Steinebach (1981).     

On the choice of the number of blocks with the incremental EM algorithm for the fitting of normal mixtures

The EM algorithm is a popular method for parameter estimation in situations where the data can be viewed as being incomplete. As each E-step visits each data point on a given iteration, the EM algorithm requires considerable computation time in its application to large data sets. Two versions, the incremental EM (IEM) algorithm and a sparse version of the EM algorithm, were proposed recently by Neal R.M. and Hinton G.E. in Jordan M.I. (Ed.), Learning in Graphical Models, Kluwer, Dordrecht, 1998, pp. 355–368 to reduce the computational cost of applying the EM algorithm. With the IEM algorithm, the available n observations are divided into B (B n) blocks and the E-step is implemented for only a block of observations at a time before the next M-step is performed. With the sparse version of the EM algorithm for the fitting of mixture models, only those posterior probabilities of component membership of the mixture that are above a specified threshold are updated; the remaining component-posterior probabilities are held fixed. In this paper, simulations are performed to assess the relative performances of the IEM algorithm with various number of blocks and the standard EM algorithm. In particular, we propose a simple rule for choosing the number of blocks with the IEM algorithm. For the IEM algorithm in the extreme case of one observation per block, we provide efficient updating formulas, which avoid the direct calculation of the inverses and determinants of the component-covariance matrices. Moreover, a sparse version of the IEM algorithm (SPIEM) is formulated by combining the sparse E-step of the EM algorithm and the partial E-step of the IEM algorithm. This SPIEM algorithm can further reduce the computation time of the IEM algorithm.     

Integer-valued moving average (INMA) process

A simple model for a stationary sequence of dependent integer-valued random variables {X_n} is given. The sequence to be called integer-valued moving average (INMA) process, is taken as the “survivals” of i.i.d. non-negative integervalued random variables. It is argued that the model’s structure reflects to some extent the mechanism generating real life data for many counting process and consequently it is useful for modelling such processes. Various properties for the special case in which {X_n} is Poisson INMA (1) process, such as the joint distribution, regression, time reversibility, along with the conditional and partial correlations, are discussed in details. Extension of the INMA of first order to higher order moving average is considered.     

多元线性模型中最优设计测度的判别准则

利用多元线性模型问题可转化为一元线性模型的方法,将Gaffke的结论推广到多元线性模型中,得到多元线性模型中最优设计测度的一个比较简单的充要条件.此条件对完全或不完全的准则函数Φ都是适用的,从而在理论上完全解决了多元线性模型中最优设计测度的判别问题.     

Hierarchical Dependency Models for Multivariate Survival Data with Censoring

A familyof partial likelihood logistic models is proposed for clusteredsurvival data that are reported in discrete time and that maybe censored. The possible dependence of individual survival timeswithin clusters is modeled, while distinct clusters are assumedto be independent. Two types of clusters are considered. First,all clusters have the same size and are identically distributed.Second, the clusters may vary in size. In both cases our asymptoticresults apply to a large number of small independent clusters.     

基于近邻截断的跳跃扩散过程波动函数的设定检验

高频数据环境下的波动函数设定检验容易受到数据中跳跃的影响。为此，本文基于近邻截断（nearest neighbor truncation）方法，利用残差构造部分和（partial sum）过程构造出波动函数参数形式的设定检验方法，并分析了该检验方法在原假设条件下的近似极限性质与自助检验步骤。所提出的波动函数设定检验方法能渐近有效的避免跳跃扩散过程的漂移项与跳跃项的影响。蒙特卡洛模拟结果表明这些检验方法对跳跃的影响具有稳健性，且具有合理的检验水平（size）和检验功效（power）。利用这些检验方法对我国的上海银行间同业拆放利率（Shibor）数据进行实证分析，结果表明本文所提出的跳跃稳健的波动函数检验方法比非跳跃稳健的波动函数检验方法具有更好的区分度。     

部分信息下生鲜农产品采购外包问题研究

针对生鲜农产品的固有属性导致的采购风险，以及企业将一些业务如物流、采购等外包给第三方物流企业（3PL，Third Party Logistics），从而专注于自身核心业务发展的现实，建立了零售商和3PL的博弈模型，对比分析了部分需求信息下3PL采购和零售商采购对零售商和3PL的最优决策、利润，以及供应链系统利润的影响。研究表明，当正向需求风险较大时，3PL对生鲜农产品实际需求的判断较准确；当需求风险较小时，零售商对生鲜农产品实际需求的判断较准确。研究还发现，在绝大部分情况下，3PL采购对供应链系统是不利的。只有当正向需求风险很大，或生鲜农产品损耗率非常大，或损失分担比例很高时，3PL采购才能够增加供应链系统的利润。然而，在3PL采购提高供应链系统利润的条件下，3PL的利润低于同等条件下零售商采购时的利润。建议此时零售商通过采取返还给3PL一定利润的方式来促使3PL同意参与采购管理，以增加零售商、3PL和供应链系统的利润，提高供应链的竞争力。