Conditioning as disintegration

Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon–Nikodym derivatives, although we all secretly perform heuristic calculations using elementary definitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information.
One way to engage in rigorous, guilt-free manipulation of conditional distributions is to treat them as disintegrating measures—families of probability measures concentrating on the level sets of a conditioning statistic. In this paper we present a little theory and a range of examples—from EM algorithms and the Neyman factorization, through Bayes theory and marginalization paradoxes—to suggest that disintegrations have both intuitive appeal and the rigor needed for many problems in mathematical statistics.     

Exchangeability, Correlation, and Bayes' Effect

We examine the difference between Bayesian and frequentist statistics in making statements about the relationship between observable values. We show how standard models under both paradigms can be based on an assumption of exchangeability and we derive useful covariance and correlation results for values from an exchangeable sequence. We find that such values are never negatively correlated, and are generally positively correlated under the models used in Bayesian statistics. We discuss the significance of this result as well as a phenomenon which often follows from the differing methodologies and practical applications of these paradigms – a phenomenon we call Bayes' effect.     

On a simple sequential decision problem

We consider a simple sequential problem that generalizes the gamble with a fair coin. A sequence [ X _n] ot {0,1} r.v.'s is observed, and at each step the gambler can bet on either 0 or 1. The sequence ( X _n) is assumed exchangeable. Except for the case of i.i.d. r.v.'s with even probability (the fair coin), there exists a strategy such that the cumulated expected gain diverges to +∞.     

A statistical treatment of the problem of division

The problem of division is one of the most important problems in the emergence of probability. It has been long considered solved from a probabilistic viewpoint. However, we do not find the solution satisfactory. In this study, the problem is recasted as a statistical problem. The outcomes of matches of the game are considered as an infinitely exchangeable random sequence and predictors/estimators are constructed in light of de Finetti representation theorem. Bounds of the estimators are derived over wide classes of priors (mixing distributions). We find that, although conservative, the classical solutions are justifiable by our analysis while the plug-in estimates are too optimistic for the winning player.Acknowledgement. The authors would like to thank the referees for the insightful and informative suggestions and, particularly, for referring us to important references.Supported by NSC-88-2118-M-259-009.Supported in part by NSC 89-2118-M-259-012.Received August 2002     

论商品价值性质

不是任何抽象劳动都形成商品的价值,而是具有社会性、交换性和补偿性的抽象劳动才形成商品的价值。形成价值的抽象劳动的社会性、交换性和补偿性同时存在,三者互为前提,相互联系。抽象劳动的社会性、补偿性和交换性在生产过程和交换过程中形成商品价值性质。商品价值性质的核心是生产者的劳动时间与社会总劳动时间的关系。价值性质范畴有助于深化和发展劳动价值论,为判断劳动是否生产商品和形成价值提供新的视角。依据商品价值性质有助于解释一些经济现象,使劳动价值论更有说服力,从而增强其生命力。     

A note on exchangeability of random variables

A sufficient condition for the induced exchangeability or partial exchangeability of linear functions of exchangeable random variables is presented. The use of this result is illustrated through the establishment of conditional exchangeability for two sets of dependent random variables that are important in constructing conditionally distribution–free test procedures for two distinctly different problems.     

浅谈进口液化天然气"互换性"对下游用户的影响

以探讨液化天然气“互换性”为出发点．分析了进口液化天然气再汽化后是否与国内管输天然气“互换”的问题．指出了如果天然气不能“互换”将对下游燃气用户可能造成的影响．通过介绍国外解决天然气互换性问题采取的一些措施．为我国处理进口LNG与国内管输天然气的互换性问题提供参考依据。     

互换性与测量技术课程的教学模式探索

互换性与测量技术是机械设计制造及自动化专业的重要专业基础课,课程特点鲜明,本文结合教学改革实践体会,着重介绍教学内容的调整和优化、教学模式的多样化,提出为适应新世纪培养创新型人才的需求而进行的一些改革,并对课程改革提出自己的看法。