Minimizing the sum of a convex function and the product of two affine functions over a convex set

An efficient branch-and-bound algorithm for minimizing the sum of a convex function and the product of two affine functions over a convex set is proposed. The branching takes place in an interval of R the bounding is a relaxation     

正态分布在不同先验下的Bayes估计及风险比较

本文讨论在均值未知,方差已知的正态分布情况下通过在共轭先验以及Jeffreys先验二种先验下的Bayes估计问题,在平方损失函数下和线性损失函数下Bayes风险的比较.数据计算可以看出,在Jeffreys先验下的Bayes风险要比在共轭先验下的Bayes风险要大,但是当样本量增大时,两者的后验风险越来越靠近.     

A Bayesian approach to the triage problem with imperfect classification

A collection of jobs (or customers, or patients) wait impatiently for service. Each has a random lifetime during which it is available for service. Should this lifetime expire before its service starts then it leaves unserved. Limited resources mean that it is only possible to serve one job at a time. We wish to schedule the jobs for service to maximise the total number served. In support of this objective all jobs are subject to an initial triage, namely an assessment of both their urgency and of their service requirement. This assessment is subject to error. We take a Bayesian approach to the uncertainty generated by error prone triage and discuss the design of heuristic policies for scheduling jobs for service to maximise the Bayes’ return (mean number of jobs served). We identify problem features for which a high price is paid in number of services lost for poor initial triage and for which improvements in initial job assessment yield significant improvements in service outcomes. An analytical upper bound for the cost of imperfect classification is developed for exponentially distributed lifetime cases.     

A Bayesian approach to the estimation of maps between Riemannian manifolds

Let Θ be a smooth compact oriented manifold without boundary, imbedded in a Euclidean space E ^s, and let γ be a smooth map of Θ into a Riemannian manifold Λ. An unknown state θ ∈ Θ is observed via X = θ + εξ, where ε > 0 is a small parameter and ξ is a white Gaussian noise. For a given smooth prior λ on Θ and smooth estimators g(X) of the map γ we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces Θ and Λ, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of γ is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.      

两个Hermitian矩阵的Hadamard乘积的特征值估计

Schur定理规定了半正定矩阵的Hadamard乘积的所有特征值的整体界限,Eric Iksoon lm在同样的条件下确定了每个特征值的特殊的界限,本文给出了Hermitian矩阵的Hadamard乘积的每个特征值的估计,改进和推广了I.Schur和Eric Iksoon Im的相应结果。     

Polygonal estimation of planar convex-set perimeter from its two projections

This paper deals with the problem of extracting qualitative and quantitative information from few tomographic projections of an object without reconstructing this object. It focuses on the extraction of quantitative information, precisely the border perimeter estimation for a convex set from horizontal and vertical projections. In the case of a multiple reconstruction, lower and upper bounds for the perimeter are established. In the case of a unique reconstruction, we give conditions and a method for constructing an inscribed polygon in a convex set only from the convex-set projections. An inequality on border perimeter is proved when a convex set is included in another one. The convergence of the polygon perimeter, when the number of vertices increases, is established for such polygons.     

An optimization-based approach for the design of Bayesian networks

Bayesian networks model conditional dependencies among the domain variables, and provide a way to deduce their interrelationships as well as a method for the classification of new instances. One of the most challenging problems in using Bayesian networks, in the absence of a domain expert who can dictate the model, is inducing the structure of the network from a large, multivariate data set. We propose a new methodology for the design of the structure of a Bayesian network based on concepts of graph theory and nonlinear integer optimization techniques.     

Border estimation of a disc observed with random errors solved in two steps

The problem of estimating the boundary of a uniform distribution on a disc is considered when data are measured with normally distributed additive random error. The problem is solved in two steps. In the first step the domain is subdivided into thin slices and the endpoints of slices are obtained within the framework of a corresponding one-dimensional problem. For the estimations implemented in that step the moment method and the maximum likelihood method are used. As there are numerical problems with calculating the variance of the estimator in the maximum likelihood approach, its good approximation is also given.     

Testing for the equality of two binomial proportions

There are two statistics one might choose when testing whether two binomial probabilities are the same. This note provides a large sample answer to Robbins' question of which is preferable.     

Assessing the lifetime performance index of Rayleigh products based on the Bayesian estimation under progressive type II right censored samples

Lifetime performance assessment is important in service (or manufacturing) industries. Hence, lifetime performance index C_L is used to measure the potential and performance of a process, where L is the lower specification limit. In this paper, assuming the conjugate prior distribution and squared-error loss function, this study constructs a Bayes estimator under the Rayleigh distribution with the progressive type II right censored sample. The Bayes estimator of C_L is then utilized to develop a credible interval in the condition of known L. Moreover, we also propose a Bayesian test to assess the lifetime performance of products. Finally, we give two examples and the Monte Carlo simulation to assess the behavior of the lifetime performance index C_L. Moreover, the purchasers can then employ the credible interval and the Bayesian test to determine whether the product performance adheres to the required level.     

具有冷贮备部件串联系统可靠性质指标的Bayes及多层Bayes分析

本文运用Bayes及多层Bayes方法对具有冷贮备部件串联系统的失效率，可靠度与平均失效时间进行了估计，最后通过随机模拟对这两种估计进行了比较分析，得出了有效结论。     

Relevance of the Bayesian paradigm for “applied probabilists”

This paper is based on an invited lecture given by the author at the ORSA/TIMS Special Interest Group on Applied Probability Conference onStatistical and Computational Problems in Probability Modeling, held at Williamsburg, Virginia, January 7–9, 1985.The theme of this paper is twofold. First, that members of the above group should be seriously concerned with issues of statistical inference — they should not stop short upon proposing a probability model. Second, that inference be undertaken via a strict adherence to the rules of probability — the Bayesian paradigm. To underscore a need for emphasizing the first theme, it may be pertinent to note that an overwhelming majority of the papers dealing with statistical and inferential issues that were presented at this conference were authored by members who did not claim to belong to the ORSA/TIMS Special Interest Group on Applied Probability.The lecture was followed by a panel discussion, with Drs. Lyle Broemeling and Edward Wegman of the Office of Naval Research as discussants. Dr. Robert Launer of the Army Research Office served as a moderator. Discussions from the floor included comments by Professors D. Harrington of Harvard University, E. Parzen of Texas A & M University, and R. Smith of Imperial College, London, England. This paper, and the comments of the panelists, are published in this volume of theAnnals of Operations Research, which is going to serve as a Proceedings of the Conference.Supported by Contract No. N00014-85-K-0202, Office of Naval Research, and Grant No. DAAG 29-84-K-0160, Army Research Office.     

A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

GARCH models are commonly used for describing, estimating and predicting the dynamics of financial returns. Here, we relax the usual parametric distributional assumptions of GARCH models and develop a Bayesian semiparametric approach based on modeling the innovations using the class of scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution. The proposed specification allows for greater flexibility in capturing the usual patterns observed in financial returns. It is also shown how to undertake Bayesian prediction of the Value at Risk (VaR). The performance of the proposed semiparametric method is illustrated using simulated and real data from the Hang Seng Index (HSI) and Bombay Stock Exchange index (BSE30).     

Optimal policies for inventory systems with two types of product sharing common hardware platforms: Single period and finite horizon

In this paper, we consider an inventory system whose products share a common hardware platform but are differentiated by two types of software. Choice of different software results in different installation cost and different selling price of the whole product. Product with different software also faces different customer demand. We investigate the optimal proportion of an order to be installed with software 1 or 2, that maximizes expected profit in the single and multiple period scenarios, respectively. The optimal policy is analytically obtained and proved to be an order-up-to policy in each scenario. Our investigation reveals that whether to replenish, and how much to replenish each product depend not only on its own initial inventory level, and system parameters, but also the initial inventory level of the other product. We perform numerical experiments using the optimal policies we have derived in the paper.     

Infinite horizon optimal policy for an inventory system with two types of product sharing common hardware platforms

We consider a periodic review inventory system and present its optimal policy in the infinite horizon setting. The optimal inventory policy that maximizes the infinite horizon expected discounted profit for the model is analytically obtained by relating to the finite horizon setting using results from variational analysis. Results are provided that elucidate the operations of the inventory system in the long run.     

加速寿命试验Bayes估计算法的改进

本文就指数分布场合恒定应力加速寿命试验及Weibull分布场合序进应力加速寿命试验中参数的Bayes估计的显式表示提出了一种有效的改进算法,从而达到了减少计算误差和节省计算时间及内存资源的目的。     

Objective Bayesian modelling of insurance risks with the skewed Student‐t distribution

Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these data sets. This work extends a methodology recently introduced in the literature by considering an extra parameter that captures the skewness of the data. In particular, a skewed Student‐t distribution is considered. Two data sets are analysed: the Danish fire losses and the US indemnity loss. The analysis is carried with an objective Bayesian approach. For the discrete parameter representing the number of the degrees of freedom, we adopt a novel prior recently appeared in the literature. Copyright © 2017 John Wiley & Sons, Ltd.     

Bayesian calibration in the estimation of the age of rhinoceros

In this paper the Bayesian approach for nonlinear multivariate calibration will be illustrated. This goal will be achieved by applying the Gibbs sampler to the rhinoceros data given by Clarke (1992, Biometrics, 48(4), 1081–1094). It will be shown that the point estimates obtained from the profile likelihoods and those calculated from the marginal posterior densities using improper priors will in most cases be similar.     

无尺作图中两个基本作图命题的直接作图

给出了《无尺作图》两个基本作图命题的直接作图,使两个基本作图命题实际作图过程中使用圆规的次数减少到13次和10次,完全抛开了《无尺作图》基础作图体系的其他命题,完成了基础作图体系的优化研究.