激光散斑相位差的条件统计分布与表面粗糙度的关系

在粗糙表面高度起伏服从高斯统计和表面服从圆型相关的情况下，分析了由弱散射体产生的远场高斯激光散斑相位差的条件统计分布与表面粗糙度的关系．     

Jackknifing in Categorical Data Analysis

Estimation of nonlinear functions of a multinomial parameter vector is necessary in many categorical data problems. The first and second order jackknife are explored for the purpose of reduction of bias. The second order jackknife of a function g(.) of a multinomial parameter is shown to be asymptotically normal if all second order partials ?²g( p )?dp_i?p_j obey a Hölder condition with exponent α>1/2. Numerical results for the estimation of the log odds ratio in a 2times2 table demonstrate the efficiency of the jackknife method for reduction of mean-square-error and the construction of approximate confidence intervals.     

模糊取式推理的R0方法

用R0蕴涵算子描述了模糊命题“若A则B”,并通过一个例子给出了运用模糊取式推理的R0方法进行推理的具体操作过程．结果表明,运用该模糊推理得到的结论是与人们的思想相吻合的．     

Grice语用学模式批判

在话语理解中 ,通过解码获得语义 ,通过推理得出说话人意图。在语用学的发展过程中 ,话语理解的重心逐渐转移到推理过程 ,Grice的推理模式就是这种发展的代表 ,认为交际中人们遵守着合作原则以及相关准则 ,违背某些准则是为了表达暗含意义 ,需要推理求得理解。然而 ,Grice过分强调暗含意义 ,而且合作原则及有关准则来源不清 ,严重地削弱了Grice推理模式的解释力。     

Perfect simulation for correlated Poisson random variables conditioned to be positive

In this paper we present a perfect simulation method for obtaining perfect samples from collections of correlated Poisson random variables conditioned to be positive. We show how to use this method to produce a perfect sample from a Boolean model conditioned to cover a set of points: in W.S. Kendall and E. Thönnes (Pattern Recognition 32(9): 1569–1586, 1999), this special case was treated in a more complicated way. The method is applied to several simple examples where exact calculations can be made, so as to check correctness of the program using ²-tests, and some small-scale experiments are carried out to explore the behaviour of the conditioned Boolean model.     

统计学发展过程中四次重要的争论及其影响

统计学发展过程中出现过几次重大的争论,这些争论在本质上可以说是一脉相承的。"政治算术"与"国势学"的争论,明确了统计学的学科性质;"描述统计学"与"推断统计学"的争论,构筑了统计学的完整体系;"经典统计学"与"贝叶斯统计学"的争论,带来了统计哲学观的新变化;信念统计学与经典统计学、贝叶斯统计学的争论,使统计推断科学化问题的研究日趋深入。正是通过这些争论完善了现代统计学的思想和方法体系。     

Marginal Regression of Gaps Between Recurrent Events

Recurrent event data typically exhibit the phenomenon of intra-individual correlation, owing to not only observed covariates but also random effects. In many applications, the population may be reasonably postulated as a heterogeneous mixture of individual renewal processes, and the inference of interest is the effect of individual-level covariates. In this article, we suggest and investigate a marginal proportional hazards model for gaps between recurrent events. A connection is established between observed gap times and clustered survival data with informative cluster size. We subsequently construct a novel and general inference procedure for the latter, based on a functional formulation of standard Cox regression. Large-sample theory is established for the proposed estimators. Numerical studies demonstrate that the procedure performs well with practical sample sizes. Application to the well-known bladder tumor data is given as an illustration.     

Confidence intervals,significance values,maximum likelihood estimates,etc. sharpened into Occam’s razors

Abstract

Confidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions.     

Empirical Uncertain Bayes Methods in Area‐level Models

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area‐level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one‐point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area‐level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson‐gamma and the binomial‐beta, and the normal‐normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well‐known expectation‐maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second‐order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.     

康德先验逻辑的基本问题

康德的先验逻辑对传统哲学特别是形而上学所运用的范畴在分类的基础上作了新的理解,指出了范畴作为思维的逻辑功能,是对感性直观的固有关系。这就决定了先验逻辑的基本问题是范畴与直观的固有关系问题。它构成先验逻辑不同于形式逻辑和思辨逻辑的根本点。