Accurate computation of single and product moments of order statistics under progressive censoring

An accurate procedure is proposed to calculate approximate moments of progressive order statistics in the context of statistical inference for lifetime models. The study analyses the performance of power series expansion to approximate the moments for location and scale distributions with high precision and smaller deviations with respect to the exact values. A comparative analysis between exact and approximate methods is shown using some tables and figures. The different approximations are applied in two situations. First, we consider the problem of computing the large sample variance–covariance matrix of maximum likelihood estimators. We also use the approximations to obtain progressively censored sampling plans for log-normal distributed data. These problems illustrate that the presented procedure is highly useful to compute the moments with precision for numerous censoring patterns and, in many cases, is the only valid method because the exact calculation may not be applicable.     

Inference and Decision Making for 21st-Century Drug Development and Approval

ABSTRACT

The cost and time of pharmaceutical drug development continue to grow at rates that many say are unsustainable. These trends have enormous impact on what treatments get to patients, when they get them and how they are used. The statistical framework for supporting decisions in regulated clinical development of new medicines has followed a traditional path of frequentist methodology. Trials using hypothesis tests of “no treatment effect” are done routinely, and the p-value < 0.05 is often the determinant of what constitutes a “successful” trial. Many drugs fail in clinical development, adding to the cost of new medicines, and some evidence points blame at the deficiencies of the frequentist paradigm. An unknown number effective medicines may have been abandoned because trials were declared “unsuccessful” due to a p-value exceeding 0.05. Recently, the Bayesian paradigm has shown utility in the clinical drug development process for its probability-based inference. We argue for a Bayesian approach that employs data from other trials as a “prior” for Phase 3 trials so that synthesized evidence across trials can be utilized to compute probability statements that are valuable for understanding the magnitude of treatment effect. Such a Bayesian paradigm provides a promising framework for improving statistical inference and regulatory decision making.     

从《了凡四训》到《训儿俗说》——关于袁了凡及其家风家训的思想史考察

袁了凡（袁黄）以其《了凡四训》闻名于世，该书亦被当作训子家书。其实，了凡所作家训并非《了凡四训》，而是《训儿俗说》。作为王龙溪（王畿）的及门弟子，了凡在思想上是阳明后学的一分子，其人生轨迹属于典型的儒家士大夫，其日常修持及著述呈现三教汇通的思想特色。了凡家风淳朴，家学深厚，以儒为宗，兼收并蓄，强调道德主义，注重积德行善，具有出世情怀，对其人格产生深刻影响。     

Probabilistic population projections for countries with generalized HIV/AIDS epidemics

In 2015, the United Nations (UN) issued probabilistic population projections for all countries up to 2100, by simulating future levels of total fertility and life expectancy and combining the results using a standard cohort component projection method. For the 40 countries with generalized HIV/AIDS epidemics, the mortality projections used the Spectrum/Estimation and Projection Package (EPP) model, a complex, multistate model designed for short-term projections of policy-relevant quantities for the epidemic. We propose a simpler approach that is more compatible with existing UN projection methods for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression and then converted to age- and sex-specific mortality rates using model life tables designed for countries with HIV/AIDS epidemics. These are then input to the cohort component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar short-run projections to Spectrum/EPP, while being simpler and avoiding multistate modelling.     

Risk Modeling of Interdependent Complex Systems of Systems: Theory and Practice

The emergence of the complexity characterizing our systems of systems (SoS) requires a reevaluation of the way we model, assess, manage, communicate, and analyze the risk thereto. Current models for risk analysis of emergent complex SoS are insufficient because too often they rely on the same risk functions and models used for single systems. These models commonly fail to incorporate the complexity derived from the networks of interdependencies and interconnectedness (I–I) characterizing SoS. There is a need to reevaluate currently practiced risk analysis to respond to this reality by examining, and thus comprehending, what makes emergent SoS complex. The key to evaluating the risk to SoS lies in understanding the genesis of characterizing I–I of systems manifested through shared states and other essential entities within and among the systems that constitute SoS. The term “essential entities” includes shared decisions, resources, functions, policies, decisionmakers, stakeholders, organizational setups, and others. This undertaking can be accomplished by building on state‐space theory, which is fundamental to systems engineering and process control. This article presents a theoretical and analytical framework for modeling the risk to SoS with two case studies performed with the MITRE Corporation and demonstrates the pivotal contributions made by shared states and other essential entities to modeling and analysis of the risk to complex SoS. A third case study highlights the multifarious representations of SoS, which require harmonizing the risk analysis process currently applied to single systems when applied to complex SoS.     

朱熹和孟子解读舜之“怨慕”的不同逻辑

对于舜之“怨慕”,朱熹作出了不同于孟子的解读。这是基于心学、理学内在逻辑的不同。孟子作为私学之儒,和孔子一样,是主张士君子的阳刚人格的,并且从性向善的人性论出发,协调义与利、公与私的关系,而以君臣父子关系都属对待关系;依此,将舜之“怨慕”解读为舜对父母的既怨又慕。朱熹则作为官学之儒,以所谓“气质之性”协调理学先驱荀子的性向恶论,以二歧化思维把天地之性、天理绝对化,以公去私,视君臣父子关系则为下对上的绝对服从关系;依此解读,舜之“怨”只能是自怨。     

需求率受推广努力水平影响的新能源汽车租赁系统协调契约

考虑由新能源汽车租赁企业和政府组成的二级系统，在需求率为随机且与推广努力水平相关的市场环境下，建立了新能源汽车租赁企业和政府之间的博弈模型，探讨了分散决策、集中决策、收益共享与成本共担契约下的最优车队配置和推广努力水平，并对三种情形下的最优决策进行了比较和分析。研究结果表明：在分散决策情况下无法实现系统协调，通过引入成本共担与收益共享组合契约，当契约参数满足一定条件时，该组合契约模型不仅可以实现系统协调而且可以使系统成员达到帕累托改进。最后通过算例分析，验证了模型了可靠性和有效性。     

多边贸易体制下中国发展中国家地位问题研究——基于历史、现实与规范的多维考察

当前,发展中国家地位问题受到国际社会的高度关注,已成为世界贸易组织改革中的主要讨论议题。然而,现行世界贸易组织多边规则体系中并没有关于“发展中国家地位”的清晰界定,“自我认定”的方式正遭受一些国家的挑战。发展中国家地位和特殊与差别待遇条款密切相关,世界贸易组织规则体系中涵盖的155项特殊与差别待遇条款为发展中国家的国内政策提供了一定的灵活性,尽管多数为“最佳努力条款”。中国的发展中国家地位兼具身份和契约的双重属性,部分发达国家迫使中国放弃发展中国家地位,本质上旨在继续维持其在国际经济秩序中的主导地位。虽然中国的发展正处于“强起来”的第三阶段,但仍须坚持发展中国家地位不动摇。放弃发展中国家地位并不等于将获得发达国家的自动接纳,相反,还会影响到在其他国际组织和国际事务中的角色扮演,中国的发展离不开广大发展中国家的支持。当然,坚持发展中国家地位并不等于需要和其他发展中成员享受完全一致的差别待遇,在后续谈判中,中国可以保持一定的灵活性。在国际治理中,中国也将继续为国际社会的发展提供解决方案,树立负责任大国形象。     

信息技术与高中数学课程整合探究

信息技术与数学课程整合已成为必然趋势,各种教学辅助软件的出现使教师应接不暇。数学软件Maple凭借其简单的操作和强大的功能等优势被越来越多的数学教师作为辅助教学软件。本文用数学实验的方法介绍了Maple在高中数学教学中的几个应用实例,并对信息技术与课程整合与传统教学法之间的优缺点进行了比较。     

先秦的“法治”思想和实践考量

先秦法家在与儒家“礼治”的争论中提出“法治”思想,并与战国时期富国强兵的国家策略结合,变法图存的“法治”实践此起彼伏。其中最为成功的是秦国的商鞅变法,秦国由此迅速崛起并最终吞并六国,建立起统一的封建国家。秦帝国的建立是“法治”思想和实践的里程碑,大秦将集权专制和“法治”相互糅合,将法家重刑思想发展到极端,走向了崇尚暴力和滥刑滥杀的野蛮恐怖境地,导致天下怨叛,秦王朝二世而亡,君权至上最终将法治引向了集权专制的死胡同。