A General Model of Random Variation

A statistical distribution of a random variable is uniquely represented by its normal-based quantile function. For a symmetrical distribution it is S-shaped (for negative kurtosis) and inverted S-shaped (otherwise). As skewness departs from zero, the quantile function gradually transforms into a monotone convex function (positive skewness) or concave function (otherwise). Recently, a new general modeling platform has been introduced, response modeling methodology, which delivers good representation to monotone convex relationships due to its unique “continuous monotone convexity” property. In this article, this property is exploited to model the normal-based quantile function, and explored using a set of 27 distributions.     

Two-Step Residual-Based Estimation of Error Variances for Generalized Least Squares in Split-Plot Experiments

In split-plot experiments, estimation of unknown parameters by generalized least squares (GLS), as opposed to ordinary least squares (OLS), is required, owing to the existence of whole- and subplot errors. However, estimating the error variances is often necessary for GLS. Restricted maximum likelihood (REML) is an established method for estimating the error variances, and its benefits have been highlighted in many previous studies. This article proposes a new two-step residual-based approach for estimating error variances. Results of numerical simulations indicate that the proposed method performs sufficiently well to be considered as a suitable alternative to REML.     

Computational schema on ridge analysis

The purpose of this paper is to revisit the response surface technique ridge analysis within the context of the “trust region” problem in numerical analysis. It is found that these two approaches inherently solve the same problem. We introduce the computational difficulty, termed the “hard case”, which originates in the trust region methods, also exists in ridge analysis but has never been formally discussed in response surface methodology (RSM). The dual response global optimization algorithm (DRSALG) based on the trust region method is applied (with a certain modification) to solving the ridge analysis problem. Some numerical comparisons against a general-purpose nonlinear optimization algorithm are illustrated in terms of examples appearing in the literature     

Statistical Inference of Adaptive Designs with Binary Responses

Adaptive designs of clinical trials are ethical alternatives when the traditional randomization becomes ethically infeasible in desperate medical situations. However, such a design creates a dependency among trial data and its statistical analysis becomes more complex than the analysis for traditional randomized clinical trials. In this article, we examine adaptive designs with dichotomous responses from two treatments and extend some commonly used statistical methods for independent data. Under a regularity condition, the estimated odds ratio and its logarithm are shown to follow asymptotically normal distributions. Moreover, the ordinary goodness-of-fit test statistic for two-by-two contingency tables with dependent data is shown to be asymptotically chi-square distributed. We also discuss the consistency of maximum likelihood estimators of the unknown parameters for a wide class of adaptive designs.     

Sequential Designs for Binary Data with the Purpose to Maximize the Probability of Response

Two kinds of sequential designs are proposed for finding the point that maximizes the probability of response assuming a binary response variable and a quadratic logistic regression model. One is a parametric optimal design approach, and the other one is a nonparametric stochastic approximation approach. The suggested sequential designs are evaluated and compared in a simulation study. In summary, the parametric approach performed very well whereas its competitor failed in some cases.     

A Shiny Update to an Old Experiment Game

ABSTRACT

Games can be a powerful tool for learning about statistical methodology. Effective game design involves a fine balance between caricature and realism, to simultaneously illustrate salient concepts in a controlled setting and serve as a testament to real-world applicability. Striking that balance is particularly challenging in response surface and design domains, where real-world scenarios often play out over long time scales, during which theories are revised, model and inferential techniques are improved, and knowledge is updated. Here, I present a game, borrowing liberally from one first played over 40 years ago, which attempts to achieve that balance while reinforcing a cascade of topics in modern nonparametric response surfaces, sequential design, and optimization. The game embeds a blackbox simulation within a shiny app whose interface is designed to simulate a realistic information–availability setting, while offering a stimulating, competitive environment wherein students can try out new methodology, and ultimately appreciate its power and limitations. Interface, rules, timing with course material, and evaluation are described, along with a “case study” involving a cohort of students at Virginia Tech. Supplementary materials for this article are available online.     

《弟子规》在学前教育阶段运用之利弊分析

随着国学热的升温，《弟子规》等蒙学教材在学前教育阶段使用成为一种广泛流行的文化现象。但是面对这种教育潮流，我们需要认真检视这类学习教材对孩子们的正负面影响。一方面《弟子规》被赋予了积极的教育价值，包括形塑儿童的仁爱之心、倡导诚信作为人际交往的准绳、培育良好的学习习惯等；另一方面它也有典型的负面效应，尤其体现在“尊卑贵贱”的等级观念、“封建奴性”的糟粕思想、“因循守旧”的生活态度等方面。鉴于此，提出从幼儿园、家庭和社会教育方面都应以扬弃的态度来合理使用。     

法院如何回应民意:一种法学方法论上的解决方案

围绕司法与民意的讨论,目前各界存在原因认知、概念认知、价值认知上的观点错位,影响民众对司法回应的肯定.作为法律适用机关的法院在回应民意上具有不同于政治机关的特点,必须以一种理性、中立的态度审慎地回应民意,做到有理有节、有所为有所不为.在回应过程中,应当根据民意的特点着重处理法意与民意、社会民意与权力意志之间的矛盾冲突关系,为此,必须在回应民意的时机选择与方法操作上遵循司法活动的基本规律.通过认定疑难案件的程序操作,使得外在的民意得以稳定化,以程序阻隔"舆论暴力";通过法律论证的操作,以普遍化、一致性与融贯性三原则检验与提升民意本身的合理性程度,以方法压缩个人恣意.法院的回应是对成熟且理性的民意的回应,建立在个案基础上的回应能逐步挽回民众对法院的信任.     

复杂环境下地震灾害应急救灾协同机制:一个实证分析

灾害应急管理是国家治理体系与治理能力建设,维护经济社会发展长治久安,以及实现"中国梦"、"两个一百年"奋斗目标的重要基石,也是中国特色社会主义制度更加巩固和优越性充分展现的战略部署。根据治理理论与协同学理论,通过对汶川、玉树等高原地震应急救灾的问卷调查和案例资料,探讨了政府主导社会基于支持保障体系的应急救灾协同机制实现路径,阐述了破坏性地震应急救灾何以协同、为何协同以与如何协同的内在逻辑及其现实要求,提出了加强灾害应急管理及科学引导社会参与救灾等优化对策。     

乡规民约何时出现——一个关于乡村治理的分析框架

学界对乡规民约的研究已经连篇累牍,但关于成文化的乡规民约何时出现仍颇有争议,大多学者倾向于认为北宋时期出现的《吕氏乡约》为最早的乡规民约,也有学者认为东汉已然出现早期的乡规民约,以1974年在湖北江陵凤凰山十号汉墓中出土的一枚汉景帝初年的《中舨共侍约》的木牍为文本,在分析西汉乡村农业生产水平和方式的基础上,对最早出现的乡规民约提出新的解读,认为成文化的乡规民约早在西汉时期就已经出现了。