ON THE INDEPENDENCE OF THE SAMPLE MEAN AND TRANSLATION-INVARIANT STATISTICS FOR MATRIX NORMAL DISTRIBUTIONS

We present an explicit characterization of the joint dependency structure of an n×p matrix normal random matrix such that the p-dimensional sample mean vector is independent of all translation invariant statistics.     

ELICITING A DIRECTED ACYCLIC GRAPH FOR A MULTIVARIATE TIME SERIES OF VEHICLE COUNTS IN A TRAFFIC NETWORK

The problem of modelling multivariate time series of vehicle counts in traffic networks is considered. It is proposed to use a model called the linear multiregression dynamic model (LMDM). The LMDM is a multivariate Bayesian dynamic model which uses any conditional independence and causal structure across the time series to break down the complex multivariate model into simpler univariate dynamic linear models. The conditional independence and causal structure in the time series can be represented by a directed acyclic graph (DAG). The DAG not only gives a useful pictorial representation of the multivariate structure, but it is also used to build the LMDM. Therefore, eliciting a DAG which gives a realistic representation of the series is a crucial part of the modelling process. A DAG is elicited for the multivariate time series of hourly vehicle counts at the junction of three major roads in the UK. A flow diagram is introduced to give a pictorial representation of the possible vehicle routes through the network. It is shown how this flow diagram, together with a map of the network, can suggest a DAG for the time series suitable for use with an LMDM.     

论物权法之区分原则

物权行为的独立性决定了区分原则的必然存在.区分原则,不是物权变动与原因行为的区分,而是引起物权变动的物权行为与原因行为即债权行为的区分.区分原则无论在理论或实践上均有极其重要的意义,因而在即将通过的物权法中,应确立区分原则的重要地位.     

Causal Reasoning from Longitudinal Data*

Abstract. This paper reviews some of the key statistical ideas that are encountered when trying to find empirical support to causal interpretations and conclusions, by applying statistical methods on experimental or observational longitudinal data. In such data, typically a collection of individuals are followed over time, then each one has registered a sequence of covariate measurements along with values of control variables that in the analysis are to be interpreted as causes, and finally the individual outcomes or responses are reported. Particular attention is given to the potentially important problem of confounding. We provide conditions under which, at least in principle, unconfounded estimation of the causal effects can be accomplished. Our approach for dealing with causal problems is entirely probabilistic, and we apply Bayesian ideas and techniques to deal with the corresponding statistical inference. In particular, we use the general framework of marked point processes for setting up the probability models, and consider posterior predictive distributions as providing the natural summary measures for assessing the causal effects. We also draw connections to relevant recent work in this area, notably to Judea Pearl's formulations based on graphical models and his calculus of so‐called do‐probabilities. Two examples illustrating different aspects of causal reasoning are discussed in detail.     

自动控制专业英语的教学改革探索

专业英语在选材上要重视先进性 ,在编排上力求系统性 ,注意贯穿自动化专业的主要专业课 ,如电力电子技术、模糊控制、神经网络、离散控制、微机控制技术、PLC、过程自动化、现代控制理论、楼宇自动化与智能大厦等 ,使这门课程不仅是对专业课程的总结 ,而且又是一种补充。同时增加专业英语知识 ,以加强对学生专业英语技能的培养 ,提高全面素质。具体教学中要明确教学目的 ,内容和方式 ,让学生自主选择。     

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。     

Uncertain Numbers and Uncertainty in the Selection of Input Distributions—Consequences for a Probabilistic Risk Assessment of Contaminated Land

Risks from exposure to contaminated land are often assessed with the aid of mathematical models. The current probabilistic approach is a considerable improvement on previous deterministic risk assessment practices, in that it attempts to characterize uncertainty and variability. However, some inputs continue to be assigned as precise numbers, while others are characterized as precise probability distributions. Such precision is hard to justify, and we show in this article how rounding errors and distribution assumptions can affect an exposure assessment. The outcome of traditional deterministic point estimates and Monte Carlo simulations were compared to probability bounds analyses. Assigning all scalars as imprecise numbers (intervals prescribed by significant digits) added uncertainty to the deterministic point estimate of about one order of magnitude. Similarly, representing probability distributions as probability boxes added several orders of magnitude to the uncertainty of the probabilistic estimate. This indicates that the size of the uncertainty in such assessments is actually much greater than currently reported. The article suggests that full disclosure of the uncertainty may facilitate decision making in opening up a negotiation window. In the risk analysis process, it is also an ethical obligation to clarify the boundary between the scientific and social domains.     

论当代中国司法独立的价值定位

全球化不仅对当代中国经济、政治、文化、社会生活等方面带来巨大的影响,而且也对中国法治建设提出了严峻挑战,其中至关重要的一个领域就是对司法独立制度建设方面的挑战。面对波澜壮阔的法律全球化浪潮,我们应该从中国的国情出发,在现行宪政的体制下,完善我国的司法独立制度,而不是全盘接受西方司法独立的政治体制及其所谓西方法律理想图景并根据它们去设计中国的法制未来。     

心态史视角下的孙宝琦与辛亥山东独立

辛亥革命时期,末任山东巡抚孙宝琦既效忠于清廷,又对革命党人持有恻隐,希望清廷与革命党人实现政治和解。但是,他面对省内的独立呼声和北方清廷的双重压力,无法从容转圜,从而陷入彷徨不定的心态纠结中。孙宝琦先是被迫宣布山东独立,当袁世凯指使第五镇反对独立后,孙宝琦即秉承袁世凯旨意,宣布取消独立。山东独立的波折造成了孙宝琦政治人格的分裂,使其长期受到负面评论,但是客观上却使山东避免了南北冲突的战火,因而应当予以充分理解。