A Unified Approach to the Characterization of Equivalence Classes of DAGs, Chain Graphs with no Flags and Chain Graphs

Abstract.  A Markov property associates a set of conditional independencies to a graph. Two alternative Markov properties are available for chain graphs (CGs), the Lauritzen–Wermuth–Frydenberg (LWF) and the Andersson–Madigan– Perlman (AMP) Markov properties, which are different in general but coincide for the subclass of CGs with no flags . Markov equivalence induces a partition of the class of CGs into equivalence classes and every equivalence class contains a, possibly empty, subclass of CGs with no flags itself containing a, possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov equivalence classes of CGs can be naturally characterized by means of the so-called largest CGs , whereas a graphical characterization of equivalence classes of DAGs is provided by the essential graphs . In this paper, we show the existence of largest CGs with no flags that provide a natural characterization of equivalence classes of CGs of this kind, with respect to both the LWF- and the AMP-Markov properties. We propose a procedure for the construction of the largest CGs, the largest CGs with no flags and the essential graphs, thereby providing a unified approach to the problem. As by-products we obtain a characterization of graphs that are largest CGs with no flags and an alternative characterization of graphs which are largest CGs. Furthermore, a known characterization of the essential graphs is shown to be a special case of our more general framework. The three graphical characterizations have a common structure: they use two versions of a locally verifiable graphical rule. Moreover, in case of DAGs, an immediate comparison of three characterizing graphs is possible.     

随机变量投影的一种应用

利用随机变量的投影关系,定义了偏方差矩阵,从而导出了逆方差阵元素的一种形式在随机变量是正态的条件,它为判别条件独立性有方便的操作办法。     

SO42-/TiO2催化合成乙酸乙酯的实验设计

SO4^2-／TiO2固体超强酸薄膜化催化剂能完全代替浓硫酸作催化剂,用乙酸、乙醇来合成乙酸乙酯。在膜催化器上,考察了薄膜化催化剂对乙醇和乙酸合成乙酸乙酯的催化性能。结果表明,薄膜化催化剂显著提高了催化活性;当n（乙醇）：n（乙酸）=1．5：1,原料流量3．0mL／h,在反应温度为110℃时,乙酸乙酯产率可达94．8％,且薄膜催化剂的处理很方便,催化剂再生后可重复使用,不污染环境。     

Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics

This paper concerns the geometric treatment of graphical models using Bayes linear methods. We introduce Bayes linear separation as a second order generalised conditional independence relation, and Bayes linear graphical models are constructed using this property. A system of interpretive and diagnostic shadings are given, which summarise the analysis over the associated moral graph. Principles of local computation are outlined for the graphical models, and an algorithm for implementing such computation over the junction tree is described. The approach is illustrated with two examples. The first concerns sales forecasting using a multivariate dynamic linear model. The second concerns inference for the error variance matrices of the model for sales, and illustrates the generality of our geometric approach by treating the matrices directly as random objects. The examples are implemented using a freely available set of object-oriented programming tools for Bayes linear local computation and graphical diagnostic display.     

A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0≤p≤1) or may continue to serve the next unit, if any, with probability q(=1−p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues.     

B2C电子商务顾客满意度测评研究

文章在参考已有研究成果的基础上,构建了B2C电子商务顾客满意度测评模型及其评价指标体系,并运用模糊综合评判法对某电子商务公司进行实证测评,最后对测评结果进行分析,并提出相应的对策以提升顾客满意度.     

特低渗透油藏 CO2 驱室内实验研究

针对大庆外围油田特低渗透油藏剩余油潜力大、井网加密效益差、水驱采收率低等问题，提出了特低渗透油藏 CO2驱技术。通过细管实验和天然岩芯 CO2 驱油实验，确定了 CO2 与高台子油田原油的最小混相压力，评价了特低渗透砂岩油藏 CO2 驱油效果。实验结果表明，CO2 驱可以应用于高台子油田，并取得较好的驱油效果。当天然岩芯空气渗透率为0.58 mD 时，在水驱基础上，气驱可以进一步提高采收率 8% 以上，特低渗透油藏实施 CO2 驱油技术是可行的。     

Distribution of the two‐sample t‐test statistic following blinded sample size re‐estimation

We consider the blinded sample size re‐estimation based on the simple one‐sample variance estimator at an interim analysis. We characterize the exact distribution of the standard two‐sample t‐test statistic at the final analysis. We describe a simulation algorithm for the evaluation of the probability of rejecting the null hypothesis at given treatment effect. We compare the blinded sample size re‐estimation method with two unblinded methods with respect to the empirical type I error, the empirical power, and the empirical distribution of the standard deviation estimator and final sample size. We characterize the type I error inflation across the range of standardized non‐inferiority margin for non‐inferiority trials, and derive the adjusted significance level to ensure type I error control for given sample size of the internal pilot study. We show that the adjusted significance level increases as the sample size of the internal pilot study increases. Copyright © 2016 John Wiley & Sons, Ltd.