On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

三螺旋创新模式的理论探讨

基于非线性网状创新模型提出的“三螺旋场”和“三螺旋循环”概念进一步推进了三螺旋创新模式的理论研究。三螺旋场概念旨在解释在大学、产业和政府三股螺旋之间存在的相对独立和彼此作用的本质，说明三螺旋的生成原理、静态表现和动态演化特征。三螺旋的生成原理在于创新过程的非线性本质和多主体特征，静态表现为“内核外场模型”，而动态演化过程则在于纵向进化和横向循环。发生在三股螺旋之间的三螺旋循环揭示了在大学、产业和政府之间以人员、信息和产品流动为特征的相互作用和运行机制。     

再论科技进步与社会发展之间的非线性关系

流行的观点认为,科技进步与社会发展二者之间具有相互肯定的对应关系,即社会发展的历史就是科技进步的历史,科技进步必然导致社会发展,科技越进步,社会越发展,科技每前进一步,社会就相应地发展一步。本文通过对传统的社会发展理念与科技进步的负面效应进行分析,批判了这种对社会发展与科技进步二者之间的关系只作线性把握的局限,指出在科技进步与社会发展之间存在着极其复杂的非线性关系。     

Generalized Leverage and its Applications

The generalized leverage of an estimator is defined in regression models as a measure of the importance of individual observations. We derive a simple but powerful result, developing an explicit expression for leverage in a general M -estimation problem, of which the maximum likelihood problems are special cases. A variety of applications are considered, most notably to the exponential family non-linear models. The relationship between leverage and local influence is also discussed. Numerical examples are given to illustrate our results     

化学反应中的非线性现象

本文以“水中花园”和“化学振荡”等实验事实,论述了化学反应中的自然分形和自组织过程等非线性现象.     

Economics of Radiation Protection: Equity Considerations

In order to implement cost-benefit analysis of protective actions to reduce radiological exposures, one needs to attribute a monetary value to the avoided exposure. Recently, the International Commission on Radiological Protection has stressed the need to take into consideration not only the collective exposure to ionising radiation but also its dispersion in the population. In this paper, by using some well known and some recent results in the economics of uncertainty, we discuss how to integrate these recommendations in the valuation of the benefit of protection.     

Correlated random effects regression analysis for a log-normally distributed variable

In regression analysis, it is assumed that the response (or dependent variable) distribution is Normal, and errors are homoscedastic and uncorrelated. However, in practice, these assumptions are rarely satisfied by a real data set. To stabilize the heteroscedastic response variance, generally, log-transformation is suggested. Consequently, the response variable distribution approaches nearer to the Normal distribution. As a result, the model fit of the data is improved. Practically, a proper (seems to be suitable) transformation may not always stabilize the variance, and the response distribution may not reduce to Normal distribution. The present article assumes that the response distribution is log-normal with compound autocorrelated errors. Under these situations, estimation and testing of hypotheses regarding regression parameters have been derived. From a set of reduced data, we have derived the best linear unbiased estimators of all the regression coefficients, except the intercept which is often unimportant in practice. Unknown correlation parameters have been estimated. In this connection, we have derived a test rule for testing any set of linear hypotheses of the unknown regression coefficients. In addition, we have developed the confidence ellipsoids of a set of estimable functions of regression coefficients. For the fitted regression equation, an index of fit has been proposed. A simulated study illustrates the results derived in this report.     

Optimal acceptance sampling for modules F and F1 of the European Measuring Instruments Directive

ABSTRACT

Acceptance sampling plans offered by ISO 2859-1 are far from optimal under the conditions for statistical verification in modules F and F1 as prescribed by Annex II of the Measuring Instruments Directive (MID) 2014/32/EU, resulting in sample sizes that are larger than necessary. An optimised single-sampling scheme is derived, both for large lots using the binomial distribution and for finite-sized lots using the exact hypergeometric distribution, resulting in smaller sample sizes that are economically more efficient while offering the full statistical protection required by the MID.     

技术创新的复杂性思考

技术创新是当代技术进步的重要源泉,是知识经济时代的主要标志。技术创新复杂性是近年来关心技术创新和管理组织建设的学者提出的概念。从非线性思维视角分析了技术创新的定义及组织过程,在对技术创所具有的整体性、不确定性及非线性等特点进行阐述的基础上,指出了技术创新是个复杂的系统过程。对技术创新的层次、内部非线性作用、自组织性及其演化性进行了辨析,为技术创新的研究方法提供了一个新的视域。