SHOULD WE ESTIMATE THE PROBABILITY OF CORRECT SELECTION?

Various authors, given k location parameters, have considered lower confidence bounds on (standardized) dserences between the largest and each of the other k - 1 parameters. They have then used these bounds to put lower confidence bounds on the probability of correct selection (PCS) in the same experiment (as was used for finding the lower bounds on differences). It is pointed out that this is an inappropriate inference procedure. Moreover, if the PCS refers to some later experiment it is shown that if a non-trivial confidence bound is possible then it is already possible to conclude, with greater confidence, that correct selection has occurred in the first experiment. The short answer to the question in the title is therefore ‘No’, but this should be qualified in the case of a Bayesian analysis.     

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.     

全面建设小康社会与加快民族地区发展

民族地区地域广大 ,资源丰富 ,潜在市场广阔 ,在全面建设小康社会中具有十分重要的战略地位。同时 ,民族地区经济社会发展的滞后又给全面建设小康社会带来了许多困难。只有切实克服这些困难和问题 ,才能有效地推进全面建设小康社会的伟大事业。应加大国家的扶持力度 ,认真贯彻党的民族政策 ,解放思想 ,发挥优势 ,依靠科技进步 ,采取一系列措施 ,实现民族地区的跨越式发展。     

跨跃式发展是黑龙江省民族地区全面建设小康社会的关键

本文在分析黑龙江省民族地区社会经济发展存在的差距基础之上,提出跨跃式发展是黑龙江省实现全面建设小康社会的关键,同时就促使民族地区社会经济跨跃式发展阐述了自己的看法。     

论我国民族地区的跨越式发展

跨越式发展是民族发展的一种形式,也是加快我国民族地区经济文化发展的有效途径。文章结合我国国情,分析了我国民族地区要实现跨越式发展的原因和条件,并提出了具体措施和建议。     

边限检验理论及几点讨论

检验经济变量之间长期关系的协整技术要求变量是同阶单整的,这不可避免地涉及一定程度的预检验问题,而预检验问题会增加变量间长期关系分析的不确定性。当不能确定变量的单整类型时,边限检验理论提出了一个可以直接检验一个变量和一组解释变量之间长期关系的新方法。在介绍了边限检验方法中基本的VAR模型和假设及边限检验方法中用到的重要统计量——Wald统计量和T统计量及它们各自的渐近分布形式后,说明了边限检验理论在理论和实际运用当中需要注意的几个问题,最后通过实例分析说明了边限检验理论的运用。     

Kiefer–Wolfowitz algorithm under quasi-associated random errors

In this article, we study the algorithm of Kiefer–Wolfowitz underquasi-associated random errors. We establish the complete convergence and obtain an exponential bound. Additionally, we build a confidence interval for the minimum. Numerical examples are sketched out to confirm the theoretical results and show the accuracy of the algorithm.     

Stochastic Bounds with a Low Rank Decomposition

We investigate how we can bound a discrete time Markov chain (DTMC) by a stochastic matrix with a low rank decomposition. In the first part of the article, we show the links with previous results for matrices with a decomposition of size 1 or 2. Then we show how the complexity of the analysis for steady-state and transient distributions can be simplified when we take into account the decomposition. Finally, we show how we can obtain a monotone stochastic upper bound with a low rank decomposition.