Empirical likelihood based goodness-of-fit testing for generalized linear mixed models

In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that is self scale invariant and then does not involve estimating limiting variance of the test statistic to avoid deteri- orating power of test. Furthermore, the bias correction makes the limit to be a process in which every variable is standard chi-squared. This simple structure of the process enables us to construct a Monte Carlo test proce- dure to approximate the null distribution. Thus, it overcomes a problem we encounter when classical empirical likelihood test is used, as it is asymptotically a functional of Gaussian process plus a normal shift function. The complicated covariance function makes it difficult to employ any approximation for the null distribution. The test is omnibus and power study shows that the test can detect local alternatives approaching the null at parametric rate. Simulations are carried out for illustration and for a comparison with existing method.     

基于Spearman的rho的Copula参数模型的选择

从Spearman的rho与Kendall的tau的关系入手,讨论了一类二元Copula参数模型的选择问题.由于这类二元Copula参数模型的Spearman的rho与Kendall的tau存在某种函数关系,模型选择问题转化为了曲线拟合检验问题.对于正态Copula、Frank-Copula,FGM-Copula、B11-Copula等这类Copula参数模型,说明了两种情况下进行模型选择的方法,并对中国股市的上证指数与深证综指作了实证分析,结果表明两者存在着较强的正相关性,相关性模型选取B11-Copula参数模型最合适.     

基于期货、期权与现货组合的采购决策和风险控制研究

针对企业大宗原材料采购容易受到上游价格和下游需求的不确定性影响这一问题,本文以制造商(或分销商)多阶段采购决策为研究对象,建立了包含期货、期权和现货三种采购方式的多阶段组合采购决策模型,以此来应对采购中的价格风险和库存风险.结合某钢构厂原材料采购问题,采用蒙特卡罗仿真方法进行求解.通过对比组合方式与现货方式的求解结果,证明了组合采购方式能够在各种采购环境下为采购商带来更高更稳定的利润,所提出的组合采购决策模型能够有效的规避风险.     

治愈率模型在屏蔽数据可靠性分析中的应用研究

针对传统方法中的不足,在引入标准治愈率模型的基础上,提出在屏蔽数据可靠性分析中应用一种扩展的治愈率模型的建模方法;分析证明了利用该方法进行建模分析时仅需对模型作较少的前提假设,在信息不足的情况下能够识别出伴随变量对系统寿命分布的影响,进而有效提高模型估计的稳健性.通过运用基于Gibbs抽样的MCMC方法动态模拟出相关参数后验分布的马尔可夫链,给出随机截尾条件下模型参数的贝叶斯估计;实例分析的结果,证明了该模型在可靠性应用中的直观性与有效性.     

Chain Length Distributions of Polyolefins Made in Stopped‐Flow Reactors for Non‐Instantaneous Site Activation

We developed an analytical solution to describe how the chain length distribution (CLD) of polymers made with coordination polymerization catalysts vary as a function of time for very short polymerizations considering non‐instantaneous site activation. This solution is an extension of our previous analytical expression for instantaneous site activation. We validated the analytical solution with dynamic Monte Carlo simulation and obtained excellent agreement. Simulation results indicate that, unless the catalyst activation rate is much lower than the propagation rate, it will have only a minor effect on the initial shape of the CLD of polymers made in stopped‐flow reactors (SFR). We also show how incorrect polymerization kinetic parameters may be estimated when assuming instantaneous site activation when this hypothesis is not applicable to the polymerization data under investigation.

     

Development of a protocol for small beam bi-dimensional dose distribution measurements with radiochromic films

Gafchromic™ films have become popular due to their ease of use and their near water equivalence. This last property is crucial for stereotactic small beam dosimetry as demonstrated in recent papers. An accurate bi-dimensional dose measurement with Gafchromic™ films is very challenging mainly because of the non-uniformity response of flatbed scanners (used for films digitalization) and their own non-uniformity. The first proposal of this work is to develop bi-dimensional protocol for small beams and evaluate the associated uncertainty. The second proposal is to validate this protocol for the bi-dimensional measurements of treatment plans performed with the CyberKnife^® system.First, the uniformity of an Epson V700 flatbed scanner and a batch of EBT3 Gafchromic™ films has been investigated. A “four films” dosimeter was designed to reduce the errors (statistic and systematic) due to their non-uniformity. Then, the “four films” dosimeter protocol in both a homogeneous (RW3 material) and heterogeneous (RW3, lung-like and bone-like materials) phantoms has been used to measure the bi-dimensional dose distributions of three simple CyberKnife^® treatment plans. Two tumor locations (middle of the lung and near lung/bone interface) were considered for the heterogeneous phantom. These plans were achieved with the 10 mm fixed collimator and modeled with the PENELOPE Monte Carlo code in order to calculate accurate dose distributions. Finally, the “four films” bi-dimensional dose distributions were compared to the PENELOPE Monte Carlo simulations.Regarding the uncertainty associated to the bi-dimensional dose measurement protocol, the relative standard deviation σ_D on the dose was 1.2% in the range from 0.5 to 4.0 Gy. Regarding the protocol validation on CyberKnife^® treatment plans, a very good agreement was found with all measurement points passing the {3% - 3 mm} Gamma Index criteria.     

高光谱检测复杂混合溶液的Monte Carlo仿真研究

为了克服传统光谱检测复杂混合溶液的分析方法中光谱重叠严重、信噪比低的缺点,本工作提出将高光谱法引入复杂混合溶液的检测。因为高光谱法可以利用多模式光子所携带的被测物质多种光学性质的信息进行溶液成分含量分析,与传统光谱检测方法仅利用被测物质单一吸收特性的变化相比,高光谱法同时还可利用空间信息增加光谱信号的信噪比,提高建模精度和可靠性。为了验证高光谱检测复杂混合溶液的可行性,本工作利用Monte Carlo模拟了脂肪乳Intralipid-墨水Ink模型在650～1 100nm范围内漫反射光强的分布情况,得到了复杂混合溶液的漫反射光强分布随波长变化有明显区别的现象,证明了高光谱法能够同时利用被测物质多种光学特性(如吸收、散射、各向异性因子)随波长变化的关系提高光谱信号的信噪比,有望显著增强对复杂混合溶液成分的分析能力。     

A Gridding Method for Bayesian Sequential Decision Problems

This article introduces a numerical method for finding optimal or approximately optimal decision rules and corresponding expected losses in Bayesian sequential decision problems. The method, based on the classical backward induction method, constructs a grid approximation to the expected loss at each decision time, viewed as a function of certain statistics of the posterior distribution of the parameter of interest. In contrast with most existing techniques, this method has a computation time which is linear in the number of stages in the sequential problem. It can also be applied to problems with insufficient statistics for the parameters of interest. Furthermore, it is well-suited to be implemented using parallel processors.     

Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Lévy Processes

Lévy processes can be used to model asset return's distributions. Monte Carlo methods must frequently be used to value path dependent options in these models, but Monte Carlo methods can be prone to considerable simulation bias when valuing options with continuous reset conditions. This paper shows how to correct for this bias for a range of options by generating a sample from the extremes distribution of the Lévy process on subintervals. The method uses variance‐gamma and normal inverse Gaussian processes. The method gives considerable reductions in bias, so that it becomes feasible to apply variance reduction methods. The method seems to be a very fruitful approach in a framework in which many options do not have analytical solutions.     

基于Matlab的Poisson分布随机数的Monte carlo模拟

给出了三种随机模拟:Poisson分布随机数的方法,用Matlab7.0软件实现了对Poisson分布随机数的随机模拟,并用随机模拟的方法解决了商品销售、母鸡下蛋等实际应用问题.