AN ALGORITHMIC APPROACH TO BAYESIAN LINEAR MODEL CALCULATIONS

A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects.     

加权Ky Fan不等式

用Jessen不等式证明了加权的KyFan不等式成立，证法简短，还证明了与之相应的另一个加权不等式．     

Adaptive interval estimation in one-way random effects models

Two-stage procedures are introduced to control the width and coverage (validity) of confidence intervals for the estimation of the mean, the between groups variance component and certain ratios of the variance components in one-way random effects models. The procedures use the pilot sample data to estimate an “optimal” group size and then proceed to determine the number of groups by a stopping rule. Such sampling plans give rise to unbalanced data, which are consequently analyzed by the harmonic mean method. Several asymptotic results concerning the proposed procedures are given along with simulation results to assess their performance in moderate sample size situations. The proposed procedures were found to effectively control the width and probability of coverage of the resulting confidence intervals in all cases and were also found to be robust in the presence of missing observations. From a practical point of view, the procedures are illustrated using a real data set and it is shown that the resulting unbalanced designs tend to require smaller sample sizes than is needed in a corresponding balanced design where the group size is arbitrarily pre-specified.     

On the trimmed mean and minimax-variance L-estimation in Kolmogorov neighbourhoods

We consider the properties of the trimmed mean, as regards minimax-variance L-estimation of a location parameter in a Kolmogorov neighbourhood K() of the normal distribution: We first review some results on the search for an L-minimax estimator in this neighbourhood, i.e. a linear combination of order statistics whose maximum variance in K_t() is a minimum in the class of L-estimators. The natural candidate – the L-estimate which is efficient for that member of K_t,() with minimum Fisher information – is known not to be a saddlepoint solution to the minimax problem. We show here that it is not a solution at all. We do this by showing that a smaller maximum variance is attained by an appropriately trimmed mean. We argue that this trimmed mean, as well as being computationally simple – much simpler than the efficient L-estimate referred to above, and simpler than the minimax M- and R-estimators – is at least “nearly” minimax.     

Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T^-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.     

论中庸的伦理意蕴

孔子第一个明确提出“中庸”概念,并把“中庸”看作为“至德”。中庸,就是恪守中正之道、不偏不倚、无过无不及与中和之意。“中和”,是中庸的精髓。从伦理学层面看,中庸,在人与人、人与自然关系方面,追求“和而不同”的中和境界;在道德行为上,坚持“过犹不及”的理性精神;在道德选择上,发挥“随时而中”的权变智慧;在道德规范上,坚持“兼德而至”的辨证思维原则。     

孔子“道”范畴的哲学阐释

“道”是中国古代哲学的核心范畴之一，它在孔子思想中具有重要的地位及其意义。孔子的“道”范畴具有天道观与人道观的涵义，人道观是其重心。就人道观而言，孔子的“道”主要是指以“仁”为最高范畴的价值理论体系，它蕴涵了以“仁”为核心的道德目标；以“礼”为核心的价值准则；以“正名”为核心的政治理想；以“中庸”为核心的方法论和以“君子”为核心的理想人格。     

中庸与华夏文化“一”、“二”、“三”

"极高明而道中庸",是中华民族高度重视实践理性的反映。但是,文化的民族性和时代性等各种因素的耦合,使传统文化具有了复杂性。重视实践理性的民族性和"一"于"道"、"一"于天理、"一"于礼义的封建性在中庸思想里都有典型体现——所谓"叩其两端竭其中",就是这种"一"于"道"的封建性本体论趋向与"叩问"二元的现实实践趋向的多重交叉,形成了"一"中有"二"、"二"中有"一"、以"一"为体、以"二"为用的中庸思想结构。其缺陷是"中"与"庸"即"用"失衡、封建教义与现实实践失衡、封建教义之"一"与现实实践的一定程度的多样性之"二"失衡。我们认为,庞朴先生"中庸"即"三分"的观点,是消解这种"一、二、一"僵化结构的时代性创新,具有实践主义的现实指向。     

逐步生物等效性t检验及在药物效能评价中的应用

在医学领域中,一种新药投产前,必须确定给人服用的安全剂量和它的毒性大小;有时又需要对两种药的药效进行比较。用均值等效二次单侧检验方法,并对其逐步推广,从而对处理组与对照组进行检验,确定是否等效。逐步等效性t检验也可用在确定仿制药的食用安全区间、比较药效等等。     

论中国古代“中和”思维方式的发生

“中和”思维方式是中国古代哲学的基本思维方式之一 ,通过对“中和”思维方式发生的研究 ,不仅可以探索中国古代思维方式发生的一般规律 ,而且可以深化对中国传统文化的探讨。本文立足于中国古人的实践 ,运用辩证唯物主义的观点 ,探讨了“中和”思维方式发生的自然、社会条件 ,论述了“中和”思维方式在实践基础上生成的历史过程。