Laplace approximations to posterior moments and marginal distributions on circles,spheres, and cylinders

We extend recent work on Laplace approximations (Tierney and Kadane 1986; Tierney, Kass, and Kadane 1989) from parameter spaces that are subspaces of R^k to those that are on circles, spheres, and cylinders. While such distributions can be mapped onto the real line (for example, a distribution on the circle can be thought of as a function of an angle θ, 0 ? 0 ? 2π), that the end points coincide is not a feature of the real line, and requires special treatment. Laplace approximations on the real line make essential use of the normal integral in both the numerator and the denominator. Here that role is played by the von Mises integral on the circle, by the Bingham integrals on the spheres and hyperspheres, and by the normal-von Mises and normal-Bingham integrals on the cylinders and hypercylinders, respectively. We begin with a brief introduction to Laplace approximations and to previous Bayesian work on circles, spheres, and cylinders. We then develop the theory for parameter spaces that are hypercylinders, since all other shapes considered here are special cases. We compute some examples, which show reasonable accuracy even for small samples.     

文学之用与作家良知——以《马嘶岭血案》《那儿》为例

文学是对人的精神和心灵的抚慰与引领,是为了让人获得向上、向善、向美的力量;作家是真理的追求者,是人类生存方式的叩问者,是现存价值的怀疑者、批判者。《马嘶岭血案》《那儿》显示了文学的真正价值与作家的可贵良知。在一些知名作家丧失了真诚、良知、责任感与艺术创造力的时候,陈应松、曹征路这两个在当代文坛并不出名的作家,通过这两部作品,显示了他们的良知、追求与创作实力,并为文学赢得了自尊。     

Interpretation of Monte Carlo Simulations Using Parameter Space Plots

Multimodal distribution functions that result from Monte Carlo simulations can be interpreted by superimposing joint probability density functions onto the contour space of the simulated calculations. The method is demonstrated by analysis of the pathway of a radioactive groundwater contaminant using an analytical solution to the transport equation. Simulated concentrations at a fixed time and distance produce multimodal histograms, which are understood with reference to the parameter space for the two random variables-velocity and dispersivity. Numerical integration under the joint density function up to the contour of the analytical solution gives the probability of contaminant exceeding a target concentration. This technique is potentially more efficient than Monte Carlo simulation for low probability events. Visualization of parameter space is restricted to two random variables. Nevertheless, analyzing the two most pertinent random variables in a simulation might still offer insights into the multimodal nature of output histograms.     

统筹区域发展必要性的理论和实证分析

缪尔达尔的“地理上的二元经济结构”理论、赫希曼的“极化、涓滴效应”理论、佩鲁的“发展极”理论和梯度推移理论对统筹区域发展具有重要的理论指导意义,区域差距扩大所带来的种种矛盾及潜伏的危机与构建和谐社会所产生的冲突使统筹区域发展更为迫切。文章试图从理论和实证两个角度对统筹区域发展的必要性深入分析。     

一类二阶四点边值问题凸正解的存在性

讨论了一类二阶四点边值问题正解的存在性,给出了这一问题对应的Green函数,应用锥上的不动点定理给出了问题存在凸正解的充分条件.     

An approach to non-linear principal components analysis using radially symmetric kernel functions

An approach to non-linear principal components using radially symmetric kernel basis functions is described. The procedure consists of two steps: a projection of the data set to a reduced dimension using a non-linear transformation whose parameters are determined by the solution of a generalized symmetric eigenvector equation. This is achieved by demanding a maximum variance transformation subject to a normalization condition (Hotelling's approach) and can be related to the homogeneity analysis approach of Gifi through the minimization of a loss function. The transformed variables are the principal components whose values define contours, or more generally hypersurfaces, in the data space. The second stage of the procedure defines the fitting surface, the principal surface, in the data space (again as a weighted sum of kernel basis functions) using the definition of self-consistency of Hastie and Stuetzle. The parameters of this principal surface are determined by a singular value decomposition and crossvalidation is used to obtain the kernel bandwidths. The approach is assessed on four data sets.     

Analyzing cross-sectional and longitudinal lung-function measurements: The effects of age

The problem of interpreting lung-function measurements in industrial workers is examined. The data under discussion pertain to FEV₁ and FVC measurements in smoking and in nonsmoking groups of grain-elevator workers in British Columbia and of workers in Vancouver City Hall. Initial observations have now been enriched by longitudinal follow up data on the same groups after three and after six years. It is shown that interesting selection phenomena, favouring “fit” individuals, take place over time, with regard both to lung symptoms and lung functions. Thus cross-sectional and longitudinal studies refer to somewhat different populations. It also appears that longitudinal studies are considerably more sensitive to identifying cumulative lung damage than are corresponding cross-sectional studies. The nonlinearity of the effect of age on lung functions is noted in the longitudinal data in a number of cases, lending support to the hypothesis of association between quadratic age effect and cumulative exposure to lung insults.     

Positive embedded integration in Bayesian analysis

This paper describes how embedded sequences of positive interpolatory integration rules (PIIRs) obtained from Gauss-Hermite product rules can be applied in Bayesian analysis. These embedded sequences are very promising for two major reasons. First, they provide a rich class of spatially distributed rules which are particularly useful in high dimensions. Second, they provide a way of producing more efficient integration strategies by enabling approximations to be updated sequentially through the addition of new nodes at each step rather than through changing to a completely new set of nodes. Moreover, as points are added successive rules change naturally from spatially distributed non-product rules to product rules. This feature is particularly attractive when the rules are used for the evaluation of marginal posterior densities. We illustrate the use of embedded sequences of PIIRs in two examples. These illustrate how embedded sequences can be applied to improve the efficiency of the adaptive integration strategy currently in use.     

函数极限性质和存在性的证明

本文用归结原则将函数极限问题转化为数列极限问题去讨论,证明了函数极限性质与极限存在的判定定理,进而更清晰的刻画了函数极限与数列极根之间的关系。     

关于国家助学贷款良性循环机制的探讨

国家助学贷款自2000年启动以来,圆了无数困难学生的求学梦,产生了积极的社会影响。但国家助学贷款的发放机制、回收机制和激励机制不完善,亟待建立贷款回收信息系统和出台相应的法规来规范贷款人、高等学校和用人单位的责任和义务,通过减免部分或全部贷款来激发学生全面发展和到国家急需人才的地方去工作。