Effect of insignificant bias and its uncertainty on the coverage probability of uncertainty intervals: Part 2. Evaluation for a found insignificant experimental bias

This paper continues in studying the coverage probability of uncertainty intervals. It particularly investigates the uncertainty intervals determined in compliance with the GUM and EURACHEM Guide in case of the results uncorrected for the systematic error, since the experimental bias has been found insignificant. The problem is solved for known values of the experimental bias, its standard uncertainty and the overall standard uncertainty. The obtained findings given in graphs and tables show that coverage probability of the uncertainty intervals defined by expanded uncertainty about the uncorrected results can considerably fall below the chosen level of confidence; this depression depends only on the ratio of the bias and the overall uncertainty. The bias uncertainty does not directly influence this depression, it only determines whether the bias is significant or not and thereby determines whether the results will be corrected or not. The paper proposes three methods how to remove this coverage probability reduction: to apply a higher level of confidence in the significance test, to correct the results with the insignificant but too high biases and to compute the uncertainty intervals defined by some type of the uncertainties enlarged with the insignificant bias.     

新疆长石晶族产出的地质特征及其研究意义

介绍了长石晶簇在含水晶花岗伟晶岩和稀有金属花岗伟晶岩岩脉中产出的地质特征，并对六种长石晶簇（肉红色钾长石晶簇、白色钾长石晶簇、白色花瓣状钠长晶簇、白色阶梯状钠长石晶簇，束状钠长石晶簇和秀明板状钠长石晶簇）进行了描述，这些晶簇不仅具有阵列，收藏和观赏价值，而且对花岗伟晶岩的气液演化，矿床勘查和矿物资源的合理利用也有理论意义。     

灰色预测法的进一步推广及应用

把原始时间序列进行多次累加,产生多个新序列,研究它们之间的关系,建立多元线性(或非线性)回归模型.给定显著性水平α,对回归方程进行显著性检验,在置信度1-α下,利用微分,差分关系建立相应的高阶微分方程,从而实现对原序列的预测或控制.该方法进一步推广了灰色预测法,为时间序列建模提供了一个新手段,一些著名的微分方程模型成为这一方法的特例,最后,用该方法对中国1979年至2008年的GDP序列建立微分方程模型并进行预测.     

Considering Dependencies Amongst Genes Helps to Adjust the Significance Rank of DEGs

Lists of differentially expressed genes (DEGs) detected often show low reproducibility even in technique replicate experiments. The reproducibility is even lower for those real cancer data with large biological variations and limited number of samples. Since existing methods for identifying differentially expressed genes treat each gene separately, they cannot circumvent the problem of low reproducibility. Considering correlation structures of genes may help to mitigate the effect of errors on individual gene estimates and thus get more reliable lists of DEGs. We borrowed information from large amount of existing microarray data to define the expression dependencies amongst genes. We use this prior knowledge of dependencies amongst genes to adjust the significance rank of DEGs. We applied our method and four popular ranking algorithms including mean fold change (FC), SAM, t‐statistic and Wilcoxon rank sum‐test on two cancer microarray datasets. Our method achieved higher reproducibility than other methods across a range of sample sizes. Furthermore, our method obtained higher accuracy than other methods, especially when the sample size is small. The results demonstrate that considering the dependencies amongst genes helps to adjust the significance rank of genes and find those truly differentially expressed genes.     

Living polymers. Their discovery,characterization, and properties

The story of the discovery of living polymers is presented. Living polymers are polymers that retain their ability to propagate and grow to a desired size while their degree of termination or chain transfer is still negligible. Theoretical and mechanistic considerations are discussed. The living polymerization technique provides access to uniform polymers (Poisson molecular weight distribution) of controllable size, block copolymers, functional polymers, and star and comb-shaped polymers. The quantitative aspects of electron transfer are fully discussed. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: ix–xv, 1998     

鉴湖偏门段湖水的相异常及其生物化学意义

浙江绍兴黄酒闻名于世,论其质量以沈永和酿酒厂的产品为最佳.绍兴黄酒的水料自古至今汲自鉴湖,于是鉴湖湖水与绍兴黄酒之间关系十分密切.近年来对鉴湖湖水的微量元素进行全面分析后发现,沈永和酿酒厂采用的偏门段湖水含Mo量比其他湖段的要高得多,沈永和酿酒厂所产黄酒中M。含量也高出其他黄酒的许多倍M。能催化酿酒,又为人体必需的微量元素,所以,鉴湖偏门段湖水的Mo异常有着重要的生物化学意义.     

炼油污水处理的多元方差分析

提高炼油污水生化处理的达标率 ,气浮絮凝处理是关键。我们将某炼油厂目前使用的复合絮凝剂PAFC +HIHON与新研制的复合絮凝剂TIDI +HIHON投入工业运行对比试验。对炼油污水所含的石油类、CODcr、Ar OH等主要污染物进行监测并计算出它们的去除率。对三类指标的去除率运用多元方差分析 ,结果是应用新研制的絮凝剂去除率有显著提高 ,从而为新研制絮凝剂投入工业生产运行提供了可靠的依据     

Testing heteroscedasticity by wavelets in a nonparametric regression model

In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test.     

伪抛物线回归函数模型的建立与参数估计

在大量的实际问题中，变量与变量间的相关关系都呈现出伪抛物线状的变化规律，尤其在以投入报酬递减率为事物本质的研究中更是如此．本文通过对伪抛物线函数性质的深入分析，建立了伪抛物线回归函数模型，并根据该模型的特点，运用数值计算和解析计算相结合的方法，建立了该模型的参数估计方法，同时给出了显著性检验方法．     

罪与罚——司法公正的统计学分析

本文用统计学中的假设检验方法对司法审判中的定罪过程作一个比较分析,从另外一个角度来理解司法公正的内涵。