Nonconglomerative coherent conditional probabilities in statistical inference

Noteworthy connections among conglomerability, countable additivity and coherence are discussed in detail, reaching the conclusion that nonconglomerable conditional probabilities must not be doomed and play a significant role in statistical inference. Extended and updated version of a contributed paper presented at the International Conference on “Information Processing and Management of Uncertainty in knowledge-based systems”, IPMU 2004, Perugia, Italy.     

Graphical Models for Composable Finite Markov Processes

Abstract.  Composable Markov processes were introduced by Schweder (1970) in order to capture the idea that a process can be composed of different components where some of these only depend on a subset of the other components. Here we propose a graphical representation of this kind of dependence which has been called 'local dependence'. It is shown that the graph allows to read off further independencies characterizing the underlying Markov process. Also, some standard methods for inference are adapted to exploit the graphical representation, e.g. for testing local independence.     

参数假设检验教学中的几个问题

在概率统计教学的基础上,对参数假设检验教学中出现的学生难于理解的几个问题做了系统的总结,主要包括决策的依据,拒绝域的选择以及决策可靠性的判断,其中对做出"接受零假设"决策的可靠性给出了解释。     

Some characterizations of discrete distributions based on weak records

Let X ₁, X ₂,... be iid random variables (rv's) with the support on nonnegative integers and let (W _n , n≥0) denote the corresponding sequence of weak record values. We obtain new characterization of geometric and some other discrete distributions based on different forms of partial independence of rv's W _n and W _n+r —W _n for some fixed n≥0 and r≥1. We also prove that rv's W ₀ and W _n+1 —W _n have identical distribution if and only if (iff) the underlying distribution is geometric.     

Global sensitivity analysis with dependence measures

Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we introduce a new class of sensitivity indices based on dependence measures which overcomes these insufficiencies. Our approach originates from the idea to compare the output distribution with its conditional counterpart when one of the input variables is fixed. We establish that this comparison yields previously proposed indices when it is performed with Csiszár f-divergences, as well as sensitivity indices which are well-known dependence measures between random variables. This leads us to investigate completely new sensitivity indices based on recent state-of-the-art dependence measures, such as distance correlation and the Hilbert–Schmidt independence criterion. We also emphasize the potential of feature selection techniques relying on such dependence measures as alternatives to screening in high dimension.     

Robust pairwise multiple comparisons under short-tailed symmetric distributions

In one-way ANOVA, most of the pairwise multiple comparison procedures depend on normality assumption of errors. In practice, errors have non-normal distributions so frequently. Therefore, it is very important to develop robust estimators of location and the associated variance under non-normality. In this paper, we consider the estimation of one-way ANOVA model parameters to make pairwise multiple comparisons under short-tailed symmetric (STS) distribution. The classical least squares method is neither efficient nor robust and maximum likelihood estimation technique is problematic in this situation. Modified maximum likelihood (MML) estimation technique gives the opportunity to estimate model parameters in closed forms under non-normal distributions. Hence, the use of MML estimators in the test statistic is proposed for pairwise multiple comparisons under STS distribution. The efficiency and power comparisons of the test statistic based on sample mean, trimmed mean, wave and MML estimators are given and the robustness of the test obtained using these estimators under plausible alternatives and inlier model are examined. It is demonstrated that the test statistic based on MML estimators is efficient and robust and the corresponding test is more powerful and having smallest Type I error.     

On False Discovery and Non‐discovery Proportions of the Dynamic Adaptive Procedure

This paper studies the asymptotic behaviour of the false discovery and non‐discovery proportions of the dynamic adaptive procedure under some dependence structure. A Bahadur‐type representation of the cut point in simultaneously performing a large scale of tests is presented. The asymptotic bias decompositions of the false discovery and non‐discovery proportions are given under some dependence structure. In addition to existing literatures, we find that the randomness due to the dynamic selection of the tuning parameter in estimating the true null rate serves as a source of the approximation error in the Bahadur representation and enters into the asymptotic bias term of the false discovery proportion and those of the false non‐discovery proportion. The theory explains to some extent why some seemingly attractive dynamic adaptive procedures do not outperform the competing fixed adaptive procedures substantially in some situations. Simulations justify our theory and findings.     

民进党当局的“台独外交”与东南亚

民进党当局出于地缘战略的考虑,在东南亚重点推行“台独外交”。一些东南亚国家由于历史、地理、经济、文化等诸多因素的考虑,采取的是一种在大陆和台湾之间搞平衡的实用主义政策,因而在台湾问题上不断突破对中国的承诺,使双边关系受到影响。东南亚国家应与中国联手遏制“台独”,这不仅有利于地区的和平、稳定与繁荣,也符合东南亚各国的根本利益。     

Evidence of a new violation of the independence axiom

During the past 40 years there has been an accumulation of experimental evidence suggesting that most of the axioms of expected utility theory are liable to be systematically violated by substantial numbers of individuals. Much of this evidence has focused on failures of the independence axiom and has stimulated a number of alternative models that try to explain that evidence in various ways. This article presents a fresh experiment that looks at a different kind of violation—one that does not appear to be easily accommodated by several of the more prominent alternative models as they are currently formulated.The experimental work reported in this article was funded by Economic and Social Research Council Award No. B 00 23 2163.