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.     

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.     

论全球化背景下国际私法中的国家主权观--由国家利益本位向国际社会利益趋向的转化

主权原则是国际私法中的一项基本原则。在国际私法中长期以来都存在国家利益优先的倾向,但随着全球化趋势的日益增强,传统国际私法中的主权观已越来越不适应国际民商事交往蓬勃发展的现实。全球化带来的是全球法律文明的趋同化,由此伴随着全球共同利益的产生。国际私法作为处理国际民商事法律冲突的法律部门,必须对这种国际社会利益做出反应,把对人权的尊重和保护作为追求正义价值的基本向度。     

A Numerical Solution to the Nonhomogeneous Two-Stage MVK Model of Cancer

In this article, we describe a straightforward method for solving the probability of at least one malignant cell by time t, and the associated hazard function, in the general (i.e., nonhomogeneous) two-stage Moolgavkar-Venzon-Knudson (MVK) model of cancer. The method consists of solving four coupled ordinary differential equations derived from the Kolmogorov backward equations for this process. The relationship of this method to previously proposed solutions is discussed.     

On the preservation of copula structure under truncation

The author characterizes the copula associated with the bivariate survival model of Clayton (1978) as the only absolutely continuous copula that is preserved under bivariate truncation.     

On the logic of common belief and common knowledge

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge — whether individual or common — is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought — onlymonotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the infinitary nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they aredecidable in the logician's sense.     

顾客第一论

“顾客第一”有其特定的内涵,它充分体现社会主义企业的根本目的,因而是企业所有经营观念中的一个根本性观念,也是企业生产经营的一个根本指导思想。企业要实现其双重目的,促进物质文明和精神文明建设的发展,并树立各种现代经营观念,就必须坚持顾客第一。     

Measuring credibility of compensatory preference statements when trade-offs are interval determined

This paper studies how an overall fuzzy preference relation can be constructed in the compensatory context of the simple additive difference model, when imprecision on the trade-offs has to be taken into account. Three credibility indices of preferences are analysed and illustrated by a numerical example. Arguments are presented supporting the use of the third index, for which an interesting transitivity property (which was an open problem) is proved.     

Retirement patterns in Hong Kong: a censored regression analysis

This paper provides an overview of retirement patterns in Hong Kong on the basis of limited data. A censored regression model is used to infer the retirement age from people‘s current retirement status and their current age. This model is equivalent to a restricted probit model, and the interpretation of parameters is straightforward. The results clearly show a negative income effect on the retirement decision. The retirement age seems to be positively related to lifetime earnings but negatively related to the rate of decline of earnings with age. JEL classification: C24, J14, J26 Received May 6, 1996 / Accepted February 5, 1997