A Bayesian approach to the multivariate Behrens-Fisher problem under the assumption of proportional covariance matrices

Summary Two independent random samples of sizesN ₁ andN ₂ from multivariate normal populationsN _p (θ₁,∑₁) andN _p (θ₂,∑₂) are considered. Under the null hypothesisH ₀: θ₁=θ₂, a single θ is generated from aN _p(μ, Σ) prior distribution, while underH ₁: θ₁≠θ₂ two means are generated from the exchangeable priorN _p(μ,σ). In both cases Σ will be assumed to have a vague prior distribution. For a simple covariance structure, the Bayes factorB and minimum Bayes factor in favour of the null hypotheses is derived. The Bayes risk for each hypothesis is derived and a strategy is discussed for using the Bayes factor and Bayes risks to test the hypothesis.     

Bayes estimators for reliability measures in geometric distribution model using masked system life test data

This paper presents Bayes estimators for the reliability measures of the individual components in a multi-component systems in the presence of masked system life test data. The life time distributions of the system components are assumed to be geometric with different parameters. Two-sided Bayesian probability intervals of the parameters are also derived. Numerical simulation study is given in order to: (i) explain how one can apply the theoretical results obtained, (ii) study the influence of the sample size and masking level on the accuracy of point estimates.     

Determination of the Coordinates of the Center of a Gaussian Beam by Means of a Matrix Photodetector Using a Weighting Method

A weighting algorithm to determine the coordinates of the center of a Gaussian laser beam projected onto a matrix photodetector is considered. The influence of the internal noise of the photodetector, the maximum brightness of the signal at the beam maximum, and the beam radius on the precision of the algorithm is investigated. Recommendations on image processing are presented.     

Extremes of random fields over arbitrary domains with application to concrete rupture stresses

To find the exact probability distribution of the global maximum or minimum of a random field within a bounded domain is a pending problem even for Gaussian fields. Except for very special examples of fields, recourse must be taken to approximate reasoning or asymptotic considerations to be judged with respect to accuracy by simulations. In this paper, the problem is addressed through a functional equation that leads to the definition of a class of distribution functions that depend solely on process or field characteristics and domain quantities that can be calculated explicitly. This distribution function class is studied for Gaussian processes in earlier works by the author and it has been obtained explicitly for Gaussian fields on rectangular domains in the plane. Simulation studies show that rather good predictions are obtained for sufficiently smooth wide band Gaussian processes and fields. In this paper, the distribution function is obtained in general for Gaussian fields over arbitrary bounded domains with piecewise continuous and differentiable boundaries, and as in earlier works the distribution function is tested against empirical distribution functions obtained by simulation of sample functions of a smooth approximately Gaussian field, herein called a broken line Hino field. For completeness this particular field type is defined in appendix a and appendix b. The paper concludes with a statistical application on data for plain concrete tensile strength.     

Electron acceleration by single and double laser beams

The longitudinal electric field of single and double Gaussian laser beams are used to accelerate electrons. The longitudinal field of the single beam is concentrated on the axis and is favourable for acceleration. A set of two beams is considered. Beams run parallel, collinearly, overlap partially and have a phase difference iπ in between. As a result, the transverse components of fields cancel each other while the longitudinal components are double-fold. In both schemes, the electrons are accelerated in lengths of the Rayleigh range, which is common to the plasma-based accelerators.     

梯度折射率棒中传播的高斯光束轨迹解析解及其存在条件的讨论

本文提出光束轨迹方程的一般解，导出解析解的存在条件，推广了文献［１］的光线传播理论，文中以一特定梯度折射率棒为例，讨论了高斯光束在棒中的传播特性。     

Non-parametric empirical Bayes procedure

In this paper we introduce an empirical Bayes procedure for estimating an unknown parameter, say θ. This procedure gives the empirical Bayes estimator for θ and its associated minimum posterior risk in closed forms without estimating the unknown prior density function of θ. In such procedure the posterior probability density function of θ is not required. A sufficient statistic for θ with conditional probability density function in the one parameter exponential family is required. Instead of estimating the unknown prior density function, the marginal density function of the sufficient statistic must be estimated. As special cases the empirical Bayes estimators and their respective minimum posterior risks of the failure rate for the exponential distribution, the unknown scale parameters of Weibull and gamma distributions are obtained in simple forms as special cases. Numerical results and a simulation study are introduced to (i) investigate how the number of available past experiments and the sample size of each influence the accuracy of the empirical Bayes estimator, (ii) make a comparison between the presented procedure and the Bayes procedure when the prior probability density function of the parameter θ is gamma.     

二维轴对称折迭－组合腔CO2激光器失调时的输出光束的近场分析

给出平凹谐振腔和凹平凹谐振腔失调时光轴确定方法。在二维轴对称折迭－组合腔 激光器小角度失调运行时，对非相干并和和相干并和后的输出光束的近场强度分布做了分析和模拟。结果表明：小角度失调对4cm以内的近场影响不大，光强分布仍具有高斯状分布；对4cm以外的近场影响较大，光强分布发生相应的形变，且随着失调角度变大而变大。     

Existence of discrete-time LQG-controllers

Existence results for the LQG-controller are investigated. An infimal Riccati equation based controller may potentially give closed loop eigenvalues on the unit circle. Assuming left and right invertibility it is shown that there exists an optimal controller if and only if the Riccati equation based controller stabilizes the closed loop system after removal of all its unobservable and uncontrollable modes. Furthermore this reduced controller is the optimal controller, and its transfer function is unique. This existence condition is a considerable simplification of the more general geometric condition recently derived by Trentelman and Stoorvogel.     

抗几何失真的视频Hashing算法研究

文中提出了一种基于视频灰度直方图形状的Hashing算法,能有效抵抗各种常见的几何失真和视频处理操作.算法的鲁棒性原理如下:1)由于直方图的形状与像素位置无关,故基于直方图的视频Hashing算法能有效抵抗各种常见的几何攻击;2)由于在计算Hashing前对视频帧进行了平滑预处理,故算法对加噪攻击、模糊滤波、有损压缩等处理操作有很好的鲁棒性;3)由于计算Hashing前在时间轴上进行了低通滤波预处理,故算法能抵抗帧率变化、帧丢失等时域同步攻击.实验结果表明,所提出的Hashing算法有良好的唯一性和鲁棒性能.