Inference on a progressive type I interval-censored truncated normal distribution

In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

Cox regression of clustered event times with covariates missing not at random

Motivated by a recent tuberculosis (TB) study, this paper is concerned with covariates missing not at random (MNAR) and models the potential intracluster correlation by a frailty. We consider the regression analysis of right‐censored event times from clustered subjects under a Cox proportional hazards frailty model and present the semiparametric maximum likelihood estimator (SPMLE) of the model parameters. An easy‐to‐implement pseudo‐SPMLE is then proposed to accommodate more realistic situations using readily available supplementary information on the missing covariates. Algorithms are provided to compute the estimators and their consistent variance estimators. We demonstrate that both the SPMLE and the pseudo‐SPMLE are consistent and asymptotically normal by the arguments based on the theory of modern empirical processes. The proposed approach is examined numerically via simulation and illustrated with an analysis of the motivating TB study data.     

Approximate composite marginal likelihood inference in spatial generalized linear mixed models

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed model with spatial random effects. The likelihood function of this model cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. There are numerical ways to maximize the likelihood function, such as Monte Carlo Expectation Maximization and Quadrature Pairwise Expectation Maximization algorithms. They can be applied but may in such cases be computationally very slow or even prohibitive. Gauss–Hermite quadrature approximation only suitable for low-dimensional latent variables and its accuracy depends on the number of quadrature points. Here, we propose a new approximate pairwise maximum likelihood method to the inference of the spatial generalized linear mixed model. This approximate method is fast and deterministic, using no sampling-based strategies. The performance of the proposed method is illustrated through two simulation examples and practical aspects are investigated through a case study on a rainfall data set.     

基于随机p-鲁棒优化的国家血液战略储备库选址-库存模型

以往的救灾实践对建立国家血液战略储备体系提出了迫切要求。国家血液战略储备库的建设问题亟待解决。由于血液产品特性以及应急血液保障特性的存在,使得国家血液战略储备库的选址决策具有一定的复杂性。本文将问题定位为选址-库存问题。首先,以应急条件下血液保障及时度最高为目标,构建了一个不确定环境下考虑多情景、多血型、多阶段、带提前期、有容量限制、日常随机需求、有预算约束及协同定位的国家血液战略储备库选址-库存模型。同时,为了规避应急条件下的不确定风险,进一步构建了国家血液战略储备库选址-库存问题的随机p-鲁棒优化模型。该模型为离散非线性混合整数规划模型,难以快速精确求解。故基于模型性质,设计了相应的遗传算法。最后,设计了两组算例验证模型与算法的有效性。其中,第1组算例基于我国大陆地区31个省级血液中心与省级行政区的数据,并根据不同预算值给出6个算例,得到了国家血液战略储备库的选址-库存决策方案。第2组算例为6个不同规模的模拟算例,用来测试不同规模下的算法性能。算例结果表明：遗传算法的性能更好;鲁棒解与确定性模型最优值相差不大（最大差距≤1.08%）,可降低不确定性导致的风险。实践中,可对本文所建模型稍作改进,应用于具有类似特征的易腐品（药品、粮食等）应急物资储备库选址-库存决策。     

随机模糊折现现金流融资决策模型建立及求解

企业未来投资收益既具有随机性又表现出一定的模糊性,而将未来单位资本投资收益率定义为随机模糊变量,按照企业发展的特点将其分为低、中、高三个阶段,并在随机模糊环境下建立了融资决策模型,最后利用基于随机模糊模拟的SPSA算法对模型进行求解,结合算例对算法的有效性进行了解释。     

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.     

具有模糊旅行时间的VRP的一种混合遗传算法

传统确定性车辆路径问题是近几十年来运筹学领域研究的一个热点问题.但在许多实际的应用中,由于受客观世界中存在的不确定性因素以及人类观察、认识事物的模糊性的影响,车辆路径问题的某些参数可能是模糊的、不确定的.文中传统确定性车辆路径问题被扩展为具有模糊特征的模糊车辆路径问题.在对具有模糊旅行时间的车辆路径问题进行简单描述的基础上,构建了该问题的数学模型,并通过将模糊逻辑、模糊控制方法与传统车辆路径问题的遗传算法进行有效结合,提出了解决该问题的一种混合遗传算法.最后给出了该问题的一个计算实例,并通过随机模拟试验验证了该算法的有效性和优越性.     

震后伤员救援车辆两阶段规划模型及算法研究

不确定情景下的应急物资配送和车辆路径优化问题是目前国内研究的一大热点,其中 震后伤员运送车辆调度及路径优化问题随着近几年地震等自然灾害的频繁发生也逐渐引起人 们的重视． 本文采用聚合优化算法对灾区进行应急救援区域划分,建立了以总救援时间最短和 相对综合救援权重值最大为目标的救援车辆两阶段数学规划模型,设计了带三角函数变异的 离散型萤火虫优化算法进行求解,并与常规算法求解结果做了对比分析． 通过算例进行模拟实 验表明,所提出的模型和算法可以有效解决地震情景下的伤员救援车辆调度问题,且改进算法 的全局搜索性能更优．