Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

高阶非线性波动方程的有限差分方法

本文研究一类广泛的高阶非线性波动方程组初边值问题的有限差分格式，用离散泛函分析方法和先验估计的技巧得到了有限差分格式的收敛性。     

基于知识体系整合的元素无机化学教学改革

元素无机化学是大学化学及相关专业无机化学课程的核心内容。如何教好、学好元素无机化学的知识一直是教学工作者研究的课题。为改变教学现状，提高教学效果，培养学生的逻辑思维和科学创新能力，提出一种整合元素无机化学知识的思路，即：以化合物类型为主线对元素无机化学知识进行系统化整合，并以氧化物部分为例加以说明。     

Unbiased Bayes estimates and improper priors

Given two random variables (X, Y) the condition of unbiasedness states that:E(X |Y=y)=y andE(Y |X=x)=x both almost surely (a.s.). If the prior onY is proper and has finite expectation or non-negative support, unbiasedness impliesX=Y a.s. This paper examines the implications of unbiasedness when the prior onY is improper. Since the improper case can be meaningfully analysed in a finitely additive framework, we revisit the whole issue of unbiasedness from this perspective. First we argue that a notion weaker than equality a.s., named coincidence, is more appropriate in a finitely additive setting. Next we discuss the meaning of unbiasedness from a Bayesian and fiducial perspective. We then show that unbiasedness and finite expectation ofY imply coincidence betweenX andY, while a weaker conclusion follows if the improper prior onY is only assumed to have positive support. We illustrate our approach throughout the paper by revisiting some examples discussed in the recent literature.This work was partially supported by C.N.R. grant N.80.02970.10 (G.C.) and by C.N.R. grant altri interventi (P.V.). A preliminary draft was written while the Authors were visiting the Department of Statistics at Carnegie Mellon University.The paper is the result of close cooperation between the two authors. However subsections 3.1 and 3.3 are mainly due to G.C. while subsection 3.2 and section 4 are mainly due to P.V.     

物理化学课程“热化学”主题学习历程研究——化学师范生知识建构的文本分析

为深入了解地方性师范院校化学师范生知识建构习惯和水平，探讨他们在大学专业基础课程中的学习历程，以物理化学课程中以“融合科学读写特色”的“热化学”学案作为研究载体，研究对象在学案引导下开展自学活动，并在阅读教材和文献基础上进行科学写作。采用量表工具针对大学生自学效果和反思活动进行评价，并采用SOLO分类评价科学写作作品，采用KWL工具评价学生的科学阅读收获。结果发现研究对象学习动机不强，不擅长在新的学科知识学习中联系已有专业课程知识，基于文本学习的建构活动水平极低，可能是因为他们在应试背景下的基础知识并未形成体系，先修课程中并未培养元认知学习策略。     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.     

Secondary mathematics teachers’ meanings for measure,slope, and rate of change

This article reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. The data was collected with a validated written instrument designed to diagnose teachers' mathematical meanings. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topic of targeted professional development.     

The role of multiple solution tasks in developing knowledge and creativity in geometry

This paper describes changes in students’ geometrical knowledge and their creativity associated with implementation of Multiple Solution Tasks (MSTs) in school geometry courses. Three hundred and three students from 14 geometry classes participated in the study, of whom 229 students from 11 classes learned in an experimental environment that employed MSTs while the rest learned without any special intervention in the course of one school year. This longitudinal study compares the development of knowledge and creativity between the experimental and control groups as reflected in students’ written tests. Geometry knowledge was measured by the correctness and connectedness of the solutions presented. The criteria for creativity were: fluency, flexibility, and originality. The findings show that students’ connectedness as well as their fluency and flexibility benefited from implementation of MSTs. The study supports the idea that originality is a more internal characteristic than fluency and flexibility, and therefore more related with creativity and less dynamic. Nevertheless, the MSTs approach provides greater opportunity for potentially creative students to present their creative products than conventional learning environment. Cluster analysis of the experimental group identified three clusters that correspond to three levels of student performance, according to the five measured criteria in pre- and post-tests, and showed that, with the exception of originality, performance in all three clusters generally improved on the various criteria.     

创意团队隐性知识转移绩效影响因素的实证研究

文章采用问卷调研获取一手数据,运用PLS—SEM方法测度了各类因素对创意团队隐性知识转移绩效的影响。研究发现,PLS—SEM方法对观测数据拟合精度较高,在样本数据非正态分布、共线性等情况下仍然稳定。实证结果表明:团队情境、吸收能力、转移意愿、转化能力、媒介丰富度由大到小对创意团队隐性知识转移绩效产生正向影响,而隐性知识特性必须通过对知识源转化能力的显著负影响才能间接影响知识转移绩效。     

Objective Bayesian analysis of the Frechet stress–strength model

Several reference priors and a general form of matching priors are derived for a stress–strength system, and it is concluded that none of the reference priors is a matching prior. The study shows that the matching prior performs better than Jeffreys prior and reference priors in meeting the target coverage probabilities.