On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

On an adaptive version of the Metropolis–Hastings algorithm with independent proposal distribution

In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gåsemyr et al . [ Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis–Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to Π. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of Π.     

Optimal scaling of Metropolis algorithms: Heading toward general target distributions

The authors provide an overview of optimal scaling results for the Metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high‐dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well‐known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.     

国外票据市场的发展及对我国的启示

随着现代经济的发展 ,票据作为一种支付信用结算工具 ,其低风险、高流动性的短期投资和融资功能日益受到企业、商业银行及广大投资者的重视 ,各种票据逐渐成为企业短期融资、银行提高资产负债的流动性管理和风险管理、满足投资者短期投资需要的重要货币市场工具。分析和研究票据市场发展现状及其特点 ,对我国票据市场发展有积极的借鉴意义。     

A modified false discovery rate multiple-comparisons procedure for discrete data, applied to human immunodeficiency virus genetics

Summary.  To help to design vaccines for acquired immune deficiency syndrome that protect broadly against many genetic variants of the human immunodeficiency virus, the mutation rates at 118 positions in HIV amino-acid sequences of subtype C versus those of subtype B were compared. The false discovery rate (FDR) multiple-comparisons procedure can be used to determine statistical significance. When the test statistics have discrete distributions, the FDR procedure can be made more powerful by a simple modification. The paper develops a modified FDR procedure for discrete data and applies it to the human immunodeficiency virus data. The new procedure detects 15 positions with significantly different mutation rates compared with 11 that are detected by the original FDR method. Simulations delineate conditions under which the modified FDR procedure confers large gains in power over the original technique. In general FDR adjustment methods can be improved for discrete data by incorporating the modification proposed.     

WDM网络多播中关键器件放置问题的研究

研究了在WDM网络中,分光器件和波长变换器件随机放置的情况下,两种器件的数量分别对于多播业务阻塞率的影响．从仿真结果可以得出,增加配置有波长变换器件节点的个数可以明显地降低阻塞率,而增加配置有分光器件节点的个数在某些情况下,会导致阻塞率的增加．并深入探讨了造成这些现象的原因．     

深圳市投资率与投资效益的合理区间分析

投资、消费和净出口被喻为拉动经济发展的三驾马车。对于深圳这样一个以投资拉动为主的城市,投资在经济发展中具有重要的地位。通过对投资率和ICOR的国际比较分析,综合深圳市发展的历史阶段,可以揭示并发现深圳市的投资率与ICOR的合理区间、正确规划,以及深圳市的长远发展目标和规划。     

台湾的金融改革及其启示

要本文在分析台湾实行金融改革动因的基础上，概述了台湾金融改革的内容，评述了台湾实行金融自由化的目的－建立区域金融中心的构想，并就这一改革给大陆带来的启示作出了思考。     

引导与干预:不同汇率制度中的央行行为分析

广义汇率目标区制包括介于浮动汇率制与固定汇率制之间的所有的汇率安排,中央银行外汇市场干预的不同,决定了汇率目标区制中类型的不同。在中央银行强有力的干预下,中心汇率和目标区公开是最具吸引力的一种目标区制,其根本特性就在于其汇率形成机制的内在稳定性,从而也是构建未来人民币汇率目标区制的较好选择。     

改进的OBS长度自适应门限组装算法

现有OBS长度自适应组装算法的突发数据长度门限的选择虽然随着业务流的变化而变化,克服了固定长度门限算法输出的突发数据的突发性,但仍然没有考虑业务流的自相似特性,因此不能有效降低输出突发数据的自相似程度和分组阻塞率。针对这一问题,该文提出了一种改进的OBS长度自适应门限组装算法,能根据到达的网络业务流的自相似特性自适应地调整长度门限值。仿真结果表明:在相同的调度算法下,更能降低业务流的自相似性,分组阻塞率降低一个数量级。