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.     

关于外汇期货套期保值比率的实证研究

最佳套期保值比率(OHR)的估计方法一直是金融工程理论研究的核心问题,从最开始的幼稚法到JSE法 以及随后的很多其他改进方法,保值效率都有不同程度的提高。使用包含误差修正结构的GARCH模型估计外汇 (澳大利亚元)期货的套期保值比率。通过效率比较,证实该模型所得到的套期保值比率比起传统方法都具有更好 的降低风险能力。     

突出人才素质培养的教学模式改革

从高职教育的培养目标入手 ,就高等职业技术教育中机械类和近机类专业的技术基础课《机械设计基础》如何改革教学模式 ,培养新型人才 ,提出了以下设想 :建立具有“双师型”的教师队伍 ;装备机械设计专用教室 ;针对不同问题做小设计 ;改革考核方式     

《国际私法》课程的教学方法探讨

案例教学和差异比较法教学是适合《国际私法》课程特点的教学方式方法。其中 ,案例教学是将教学内容、教学目的和教学方法等融汇于特定的案例分析和评价的一种教学过程和教学组织架构 ,一般由案例的准备、呈现、问题、思与行、评价和回归教材 6个环节动态地建构而成 ;而差异比较法教学则是以一个特定的国家的法律为比较基准 ,通过对各被比较国家在同一问题上的法律规定作相应的对比和分析 ,找出相应的差异并进一步探索国际私法的基本原理和解决法律冲突的方法的一种教学过程和教学方法 ,一般包括准备、实体法上的差异比较、法律冲突、解决冲突的方案、冲突规范的比较、综合评价 6个步骤。教师在《国际私法》课程的教学过程中应精心设计和实施案例教学和差异比较法教学且应将二者结合运用     

Mapping water quality by local scoring

The mean density of bacteria in a water body is commonly monitored using quantal assay. This paper describes the use of local scoring in estimating the spatial distribution of mean density from quantal assay results at a set of point locations. An application to estimating the mean density of fecal conform bacteria in a coastal pond is presented. Model diagnostics based on a parametric bootstrap are also presented.     

Modelling map positional error to infer true feature location

The authors consider the issue of map positional error, or the difference between location as represented in a spatial database (i.e., a map) and the corresponding unobservable true location. They propose a fully model‐based approach that incorporates aspects of the map registration process commonly performed by users of geographic informations systems, including rubber‐sheeting. They explain how estimates of positional error can be obtained, hence estimates of true location. They show that with multiple maps of varying accuracy along with ground truthing data, suitable model averaging offers a strategy for using all of the maps to learn about true location.     

三种渠道断面结构形式的适用及经济性分析

通过对常见的田间三种渠道特性夏适应性分析,反应出推广U型砼槽的必要性。给我们今后在水利工程田间渠道结构形式的选用上,提供了帮助。     

等效法在物理教学中应用规律的探讨

本文研究了等效法在中学物理教学中的应用，并结合一些具体实例进行了分析，对中学物理教学有一定指导意义。     

Pseudo–Modelling of Outliers for Estimation of Regression And Time Series Models

This paper documents situations where the variance inflation model for outliers has undesirable properties. The model is commonly used to accommodate outliers in a Bayesian analysis of regression and time series models. The alternative approach provided here does not suffer from these undesirable properties but gives inferences similar to those of the variance inflation model when this is appropriate. It can be used with regression, time series, and regression with correlated errors in a unified way, and adheres to the scientific principle that inference should be based on the data after obvious outliers have been discarded. Only one parameter is required for outliers; it is interpretable as the a priori willingness to remove observations from the analysis.     

Defining the linear portion of a sigmoid‐shaped curve: bend points

Formulae are provided that define the ‘bend points’, the beginning and end of the essentially linear dose–response region, for the four‐parameter logistic model. The formulae are expressed in both response and dose units. The derivation of the formulae is shown in order to illustrate the general nature of the methodology. Examples are given that describe how the formulae may be used while planning and conducting bioassays. Copyright © 2003 John Wiley & Sons, Ltd.