A Unified Approach to the Approximation of Multivariate Densities

Approximation of a density by another density is considered in the case of different dimensionalities of the distributions. The results have been derived by inverting expansions of characteristic functions with the help of matrix techniques. The approximations obtained are all functions of cumulant differences and derivatives of the approximating density. The multivariate Edgeworth expansion follows from the results as a special case. Furthermore, the density functions of the trace and eigenvalues of the sample covariance matrix are approximated by the multivariate normal density and a numerical example is given     

测试实数编码遗传算法的困难度

分析了遗传算法困难度测试在遗传算法研究中的重要意义. 鉴于当前这方面的研究集 中于二进制编码遗传算法,对实数编码遗传算法的困难度测试进行了分析. 探讨了实数编码遗 传算法困难度分析的适应值与距离相关系数测试法与基于随机游走模型的相关函数测试法, 提出了最佳一阶函数逼近测试法,做了大量实验,并根据实证分析结果对三种方法进行了比较 与评价.     

Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

The paper presents a general method of designing constant-factor approximation algorithms for some discrete optimization problems with assignment-type constraints. The core of the method is a simple deterministic procedure of rounding of linear relaxations (referred to as pipage rounding). With the help of the method we design approximation algorithms with better performance guarantees for some well-known problems including MAXIMUM COVERAGE, MAX CUT with given sizes of parts and some of their generalizations.     

供应商管理库存环境下的分销网络连续近似模型

本文在现有连续近似(CA)模型的基础上,从供应商管理库存(VMI)角度出发,引入了PowerofTwo(POT)周期配送策略,构建了VMI环境下分销网络设计的CA模型。该模型的目标函数不仅包括了分销中心的建设 运营费用、运输费用,而且引进了实际中关注的存储费和订货费;该模型在确定分销网络结构的同时,也确定了各分销中心的库存策略和对其客户的配送策略。文中给出了模型的解法,利用此解法对算例进行求解,并分析了求解的结果,得出各参数变化对解的影响。     

三台平行机排序的一个复合半在线问题的算法

本文讨论一个三台平行机半在线排序问题.对预先知道工件的总加工时间和最大的工件的加工时间的复合半在线模型,我们证明了不存在半在线算法,其竞争比为4/3,并给出了一个竞争比为7/5的半在线算法,两者的差距小于0.067.     

一类含有随机参数的混沌系统的Hopf分岔研究

文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.     

Empirical Likelihood for the Additive Hazards Model with Current Status Data

We investigate empirical likelihood for the additive hazards model with current status data. An empirical log-likelihood ratio for a vector or subvector of regression parameters is defined and its limiting distribution is shown to be a standard chi-squared distribution. The proposed inference procedure enables us to make empirical likelihood-based inference for the regression parameters. Finite sample performance of the proposed method is assessed in simulation studies to compare with that of a normal approximation method, it shows that the empirical likelihood method provides more accurate inference than the normal approximation method. A real data example is used for illustration.     

Bayesian prediction of waiting times in stochastic models

The authors show how saddlepoint techniques lead to highly accurate approximations for Bayesian predictive densities and cumulative distribution functions in stochastic model settings where the prior is tractable, but not necessarily the likelihood or the predictand distribution. They consider more specifically models involving predictions associated with waiting times for semi‐Markov processes whose distributions are indexed by an unknown parameter θ. Bayesian prediction for such processes when they are not stationary is also addressed and the inverse‐Gaussian based saddlepoint approximation of Wood, Booth & Butler (1993) is shown to accurately deal with the nonstationarity whereas the normal‐based Lugannani & Rice (1980) approximation cannot, Their methods are illustrated by predicting various waiting times associated with M/M/q and M/G/1 queues. They also discuss modifications to the matrix renewal theory needed for computing the moment generating functions that are used in the saddlepoint methods.     

Integrated nested Laplace approximation for the analysis of count data via the combined model: A simulation study

The combined model accounts for different forms of extra-variability and has traditionally been applied in the likelihood framework, or in the Bayesian setting via Markov chain Monte Carlo. In this article, integrated nested Laplace approximation is investigated as an alternative estimation method for the combined model for count data, and compared with the former estimation techniques. Longitudinal, spatial, and multi-hierarchical data scenarios are investigated in three case studies as well as a simulation study. As a conclusion, integrated nested Laplace approximation provides fast and precise estimation, while avoiding convergence problems often seen when using Markov chain Monte Carlo.     

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Summary.  Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models , where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.