贝叶斯统计推断及其主要进展

贝叶斯统计推断作为现代统计分析方法的重要内容,对于统计学理论的发展具有里程碑的作用。深入总结其研究的主要进展,具有重要的现实意义。在查阅国内外重要学术研究资料的基础上,从贝叶斯统计推断的思想、与古典统计的研究思路比较和贝叶斯统计推断研究的主要进展三个方面作了综述与介绍,力图达到认识贝叶斯统计推断及其研究现状的目的。     

目前的统计形势(上)

统计学有三个相互关联的支柱 :概率数学、调查设计的一般原理、调查分析和解释的一般原理 ;统计推断的形式原理是第三支柱的一部分 ;现代概率理论的发展已在现代数学中占有丰富多采的篇章 ;调查设计与实验之间在原则上有重大差别 ;新分析方法有很大发展 ,许多统计工作无疑与各种具体测度有关 ;推断的形式理论 ,争论主要集中在概率推理方面 ;政府统计学家与社会科学研究工作者之间需要合作 ;最近 1 0多年统计思想创新进入一个新时期。     

“九五”期间统计学发展回顾与“十五”期间统计学研究的重要领域及重点课题探讨

一、“九五”期间统计学发展回顾“九五”期间 ,国内外统计学研究主要围绕统计理论的完善与发展、统计方法的应用、统计学与信息技术的结合等领域来进行。随着统计理论的不断发展 ,统计学与概率论及数学其他分支的交叉联系不断加强 ,统计学的内容体系越来越丰富。在一些前沿性领域 ,如探索性数据分析、计算机模拟、贝叶斯推断及应用、生存分析等方面的研究正在不断深入。国际统计标准分类、ＳＮＡ的完善等诸多方面的研究也已取得重大成果。具体表现为 :1 在统计理论的完善与发展方面 ,有关统计推断、随机过程、多元分析、生存分析、时间序列…     

基于混合参数先验分布的贝叶斯因子分析

因子分析模型的贝叶斯推断是贝叶斯多元统计推断理论的重要组成部分。本文通过分析因子分析模型的统计结构,构造了模型参数的混合先验分布;利用贝叶斯定理,结合模型样本似然函数和参数的先验分布推导了参数的后验分布;证明了因子载荷阵的条件后验分布为矩阵t分布,协方差阵的条件后验分布为逆Wishart分布。实证研究结果表明:由于参数先验分布的作用,贝叶斯因子分析的结论与传统的因子分析之间存在显著性的差异。     

抽样推断中比例估计的几种方法及比较

本文通过比例估计的例子，揭示了不同抽样理念、统计学派以及估计方法在抽样推断中的应用及特点，特别的分析了基于模型的抽样理念下，贝叶斯思想和极大似然思想的应用。本文反映出统计学科中，面对同一个问题有各种不同角度的理解和解决方法。     

概率论引入统计学的意义及启示

概率论联姻统计后,统计学有了质的飞跃。研究对象、应用领域大大拓展,特别是方法上由描述走向了推断,并以概率论为基础形成相对成熟的统计思想体系。文章阐述了概率论引入统计的意义,并对由此给进一步发展统计学所带来的启示作了探讨。     

《九章算术》中的统计学思想探究

《九章算术》是中国历史上最著名的一部数学经典,该书以应用问题求解的形式为成书体例,而这些问题基本都与社会经济有关,因此书中蕴涵了丰富的统计学思想。本文从统计范围和统计思想的角度对书中的统计知识进行了分析,探讨了书中诸如统计分组、抽样推断、线性回归分析及比例关系等统计理论,并据此对当时中国古代统计思想的发展状况进行了研究。     

现代贝叶斯统计理论的基本观点与研究现状

贝叶斯统计是当今世界的两大主要统计学派之一,本文系统地论述了贝叶斯统计理论的起源、基本观点及其与频率统计学派的差异,并阐述了贝叶斯统计推断的理论研究与实践应用现状。     

现代贝叶期统计理论的基本观点与研究现状

贝叶斯统计是当今世界的两大主要统计学派之一，本文系统地论述了贝叶斯统计理论的起源，基本观点及其与频率统计学派的差异，并阐述了贝叶斯统计推断的理论研究与实践应用现状。     

经验贝叶斯方法在抽样调查中的应用

经验贝叶斯方法在抽样调查中的应用搞抽样调查的人往往会提出这样一个问题：如果不巧抽到一组＂坏＂样本，应该怎样进行统计推断才好呢？要想解决这个问题，必须在抽样调查中引入数理统计学的经验贝叶斯方法。贝叶斯方法认为在讨论一个统计问题时，必须考虑总体的历史资料...     

Rényi Statistics in Directed Families of Exponential Experiments*

Rényi statistics are considered in a directed family of general exponential models. These statistics are defined as Rényi distances between estimated and hypothetical model. An asymptotically quadratic approximation to the Rényi statistics is established, leading to similar asymptotic distribution results as established in the literature for the likelihood ratio statistics. Some arguments in favour of the Rényi statistics are discussed, and a numerical comparison of the Rényi goodness-of-fit tests with the likelihood ratio test is presented.     

企业统计改革的若干热点问题再思考

一、企业统计改革面临的挑战———改革理论滞后于改革实践的要求　　 (一 )企业统计改革的主导性观点自我国改革开放以来 ,随着市场经济体制的逐步确立以及企业改革的不断深化 ,对企业统计提出了越来越高的要求。企业统计自身的改革亦蓬勃展开 ,并在企业经营活动中发挥了一定的作用。但是 ,从众多统计杂志所发表的关于企业统计改革论文看 ,企业统计改革的主导性观点仍然停留在“健全企业统计机构、完善企业统计职能、提升企业统计地位。具体对策是在企业生产、经营、管理领域全面出击 ,监督职能部门业务活动 ,参与企业决策活动。”(二 )企…     

Multivariate convex risk statistics with scenario analysis

Abstract

In this article, we introduce three new classes of multivariate risk statistics, which can be considered as data-based versions of multivariate risk measures. These new classes are multivariate convex risk statistics, multivariate comonotonic convex risk statistics and multivariate empirical-law-invariant convex risk statistics, respectively. Representation results are provided. The arguments of proofs are mainly developed by ourselves. It turns out that all the relevant existing results in the literature are special cases of those obtained in this article.     

On blest's measure of rank correlation

Blest (2000) proposed a new nonparametric measure of correlation between two random variables. His coefficient, which is dissymmetric in its arguments, emphasizes discrepancies observed among the first ranks in the orderings induced by the variables. The authors derive the limiting distribution of Blest's index and suggest symmetric variants whose merits as statistics for testing independence are explored using asymptotic relative efficiency calculations and Monte Carlo simulations.     

从统计学史解析“自由度”概念

自由度是统计学中一个十分重要而又长期没有被圆满解释的概念。对此,从统计学史角度,对皮尔逊、费歇尔有关自由度问题争论原始文献细致考察,彻底澄清了自由度概念的内涵及与其相关的统计思想,弥补了Fienberg、Stigler与陈希孺已有解释的缺陷。研究表明：皮尔逊关于卡方检验中无论总体分布已知还是其来自于样本推断统计量都具有同一分布的错误判断,导致卡方检验的准确性出现偏差,这种偏差虽被同时代少数几个统计学家察觉但他们却无法解释其根源。费歇尔提出自由度概念并结合n维几何、假设检验与最大似然方法的论证不仅修正了皮尔逊的错误,也完善了从样本统计量估计总体参数的数理逻辑。     

Data free inference with processed data products

We consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.     

On simultaneous closeness probabilities of order statistics from odd sample sizes to the population median

In this note, we present alternative derivations for the probability that an individual order statistic is closest to the target parameter among all order statistics from a complete random sample. This approach is simpler than the geometric arguments used earlier. We also provide a simple direct proof for the symmetry property of the simultaneous closeness probabilities among order statistics for the estimation of percentiles from a symmetric family. Finally, we offer an alternative simpler proof for the result that sample medians from larger odd sample sizes are Pitman closer to the population median than sample medians from smaller odd sample sizes.     

Finite-sample Resampling-based Combined Hypothesis Tests,with Applications to Serial Correlation and Predictability

This article suggests Monte Carlo multiple test procedures which are provably valid in finite samples. These include combination methods originally proposed for independent statistics and further improvements which formalize statistical practice. We also adopt the Monte Carlo test method to noncontinuous combined statistics. The methods suggested are applied to test serial dependence and predictability. In particular, we introduce and analyze new procedures that account for endogenous lag selection. A simulation study illustrates the properties of the proposed methods. Results show that concrete and nonspurious power gains (over standard combination methods) can be achieved through the combined Monte Carlo test approach, and confirm arguments in favor of variance-ratio type criteria.     

Edgeworth expansion for signed linear rank statistics with regression constants

An Edgeworth expansion with remainder o(N^?1) is obtained for signed linear rank statistics under suitable assumptions. The theorem is proved for a wide class of score generating functions including the Chi-quantile function by adapting van Zwet's methodand Does's conditioning arguments.     

Weighted Multivariate Tests of Independence

We present new tests of marginal independence for ?^d-valued random vectors. Our tests rely upon weighted Cramér–von Mises-type statistics, which are functionals of the empirical copula process based upon a random sample of size n. We establish a decomposition of this process into asymptotically independent components, and describe the tests which follow from these arguments.