Measuring the complexity of generalized linear hierarchical models

Measuring a statistical model's complexity is important for model criticism and comparison. However, it is unclear how to do this for hierarchical models due to uncertainty about how to count the random effects. The authors develop a complexity measure for generalized linear hierarchical models based on linear model theory. They demonstrate the new measure for binomial and Poisson observables modeled using various hierarchical structures, including a longitudinal model and an areal‐data model having both spatial clustering and pure heterogeneity random effects. They compare their new measure to a Bayesian index of model complexity, the effective number p_D of parameters (Spiegelhalter, Best, Carlin & van der Linde 2002); the comparisons are made in the binomial and Poisson cases via simulation and two real data examples. The two measures are usually close, but differ markedly in some instances where p_D is arguably inappropriate. Finally, the authors show how the new measure can be used to approach the difficult task of specifying prior distributions for variance components, and in the process cast further doubt on the commonly‐used vague inverse gamma prior.     

发电厂及变电所悬垂绝缘子最小片数推算

火力发电厂及变电所中悬垂绝缘子串片数的选择是电气设计中必须的步骤和容易产生混乱的难点,因此本文对此进行了研究。同时,对导体和电器选择规程中规定的发电厂及变电所悬垂绝缘子串最小片数再发电厂及变电所污秽等级重新定义后进行修订。     

Estimation of the number of studies with positive trends when studies with negative trends are present

A two-point estimator is proposed for the proportion of studies with positive trends among a collection of studies, some of which may demonstrate negative trends. The proposed estimator is the y-intercept of the secant line joining the points (a, F?(a)) and (b, F?(b)), where F?(p) is the empirical distribution function of p-values from one-tailed tests for positive trend derived from the individual studies. Although this estimator is negatively biased for any choice of the points 0 ≤ a < b ≤ 1, the bias is less than that of the previously proposed one-point estimator defined by setting b = 1. The bias of the two-point estimator is smallest when a and b approach the inflection point of the true distribution function, E [F?(p)]. The utility of the two-point estimator is demonstrated by using it to estimate the number of male-mouse liver carcinogens among carcinogenicity studies conducted by the National Toxicology Program.     

关于分圆域Q(ζ_p)类数的第一因子的行列式表示

设p是奇素数，是分圆域K＝Q（ζp）类数的第一因子。本文运用代数方法证明了：可表成p／2p-2γp与一个元素均为±1的（p-1）／2阶行列式的乘积，上述公式Carlitz和Olson的经典结果。     

局部环上欧氏空间中象对称表为对称的分解

局部环上欧氏几何中 ,正交变换表为对称问题 ,是环上欧氏几何的基本问题之一 .本文探讨的是如何将域上欧氏几何中 ,关于这一问题的结果 ,有效的转到环上来 .     

An online copy number variant detection method for short sequencing reads

The availability of the next generation sequencing (NGS) technology in today's biomedical research has provided new opportunities in scientific discovery of genetic information. The high-throughput NGS technology, especially DNA-seq, is particularly useful in profiling a genome for the analysis of DNA copy number variants (CNVs). The read count (RC) data resulting from NGS technology are massive and information rich. How to exploit the RC data for accurate CNV detection has become a computational and statistical challenge. We provide a statistical online change point method to help detect CNVs in the sequencing RC data in this paper. This method uses the idea of online searching for change point (or breakpoint) with a Markov chain assumption on the breakpoints loci and an iterative computing process via a Bayesian framework. We illustrate that an online change-point detection method is particularly suitable for identifying CNVs in the RC data. The algorithm is applied to the publicly available NCI-H2347 lung cancer cell line sequencing reads data for locating the breakpoints. Extensive simulation studies have been carried out and results show the good behavior of the proposed algorithm. The algorithm is implemented in R and the codes are available upon request.     

关于代数体函数的增长与其例外函数个数的关系

设f（z）为n值代数体函数，如果f（z）具有n＋1个Borel例外函数，则f（z）是正规增长的，其级为正整数或无穷。如果f（z）的级ρ（0＜ρ＜∞）不为整数，记P为f（z）的Borel例外函数个数，q为f（z）的亏量等于1的Nevanlinna例外值个数，则P＋q≤n．     

基于Rough集的属性约简的算法分析

研究了粗集理论中基于差别矩阵,关联矩阵的属性约简算法,分析了各种算法和原理,指出了优缺点,对以后的研究方向提出了建议.     

On a Pandemic Threshold Theorem of the Early Kermack–McKendrick Model with Individual Heterogeneity

A pandemic threshold theorem of the Kermack–McKendrick epidemic system with individual heterogeneity is proved from the definition of R ₀ by Diekmann, Heesterbeek, and Metz. The early Kermack–McKendrick epidemic model is extended to recognize individual heterogeneity, where the state variable indicates an epidemiological state or genetic, physiological, or behavioral characteristics such as risk of infection. With the basic reproduction number R ₀ for the heterogeneous population, the final size equation of the limit epidemic starting from a completely susceptible steady state at t = ?∞ has a unique positive solution if and only if R ₀  > 1. The main result is that the positive solution of the final size equation gives the lower bound of the intensity of any epidemic starting from a host population composed of susceptible and a few infected individuals who spread on a noncompact domain of the trait variable.