Design and analysis of variable fidelity experimentation applied to engine valve heat treatment process design

Summary.  When experimentation on a real system is expensive, data are often collected by using cheaper, lower fidelity surrogate systems. The paper concerns response surface methods in the context of variable fidelity experimentation. We propose the use of generalized least squares to generate the predictions. We also present perhaps the first optimal designs for variable fidelity experimentation, using an extension of the expected integrated mean-squared error criterion. Numerical tests are used to compare the performance of the method with alternatives and to investigate the robustness to incorporated assumptions. The method is applied to automotive engine valve heat treatment process design in which real world data were mixed with data from two types of computer simulation.     

Extrapolation designs and Φp-optimum designs for cubic regression on the q-ball

This paper continues earlier work of the authors in carrying out the program discussed in Kiefer (1975), of comparing the performance of designs under various optimality criteria. Designs for extrapolation problems are also obtained. The setting is that in which the controllable variable takes on values in the q-dimensional unit ball, and the regression is cubic. Thus, the ideas of comparison are tested for a model more complex than the quadratic models discussed previously. The E-optimum design performs well in terms of other criteria, as well as for extrapolation to larger balls. A method of simplifying the calculations to obtain approximately optimum designs, is illustrated.     

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.     

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。     

从社会回应模式看青少年离家出走现象

青少年离家出走问题已经成为全球性的社会现象,以西方研究社会问题的社会历史视角为基础提出的两个核心观点为"社会现象成为社会问题经历了发展的过程"和"社会各种人群或组织在社会问题的发展过程中给与了回应",从中可提炼出新的社会问题的研究模式,即社会回应模式。并通过应用中国"青少年离家出走"现象的发展过程来探讨这一社会回应模式在中国的适用性十分必要。研究发现,20世纪80年代至21世纪初期间(1980-2003年),青少年离家出走这一社会现象在中国经历了六大阶段的发展过程,并且在整个过程中,社会各人群对这一社会现象都有回应,但相应的社会回应和社会回应的研究仍存在不足。因此,对理论的进一步验证需要填充更多实证的数据,未来研究要进一步关注社会现象新一轮的发展历程和社会回应。