Quasi-Monte Carlo for Highly Structured Generalised Response Models

Highly structured generalised response models, such as generalised linear mixed models and generalised linear models for time series regression, have become an indispensable vehicle for data analysis and inference in many areas of application. However, their use in practice is hindered by high-dimensional intractable integrals. Quasi-Monte Carlo (QMC) is a dynamic research area in the general problem of high-dimensional numerical integration, although its potential for statistical applications is yet to be fully explored. We survey recent research in QMC, particularly lattice rules, and report on its application to highly structured generalised response models. New challenges for QMC are identified and new methodologies are developed. QMC methods are seen to provide significant improvements compared with ordinary Monte Carlo methods.      

On the Boolean Model of Wiener Sausages

The Boolean model of Wiener sausages is a random closed set that can be thought of as a random collection of parallel neighborhoods of independent Wiener paths in space. It describes e.g. the target detection area of a network of sensors moving according to the Brownian dynamics whose initial locations are chosen in the medium at random. In the paper, the capacity functional of this Boolean model is given. Moreover, the one- and two-point coverage probabilities as well as the contact distribution function and the specific surface area are studied. In and , the one- and two-point coverage probabilities are calculated numerically by Monte Carlo simulations and as a solution of the heat conduction problem. The corresponding approximation formulae are given and the error of approximation is analyzed. Research supported by the grant GACR 201/06/0302.     

Analysis and deconvolution of dimethylnaphthalene isomers using gas chromatography vacuum ultraviolet spectroscopy and theoretical computations

An issue with most gas chromatographic detectors is their inability to deconvolve coeluting isomers. Dimethylnaphthalenes are a class of compounds that can be particularly difficult to speciate by gas chromatography – mass spectrometry analysis, because of their significant coelution and similar mass spectra. As an alternative, a vacuum ultraviolet spectroscopic detector paired with gas chromatography was used to study the systematic deconvolution of mixtures of coeluting isomers of dimethylnaphthalenes. Various ratio combinations of 75:25; 50:50; 25:75; 20:80; 10:90; 5:95; and 1:99 were prepared to test the accuracy, precision, and sensitivity of the detector for distinguishing overlapping isomers that had distinct, but very similar absorption spectra. It was found that, under reasonable injection conditions, all of the pairwise overlapping isomers tested could be deconvoluted up to nearly two orders of magnitude (up to 99:1) in relative abundance. These experimental deconvolution values were in agreement with theoretical covariance calculations performed for two of the dimethylnaphthalene isomers. Covariance calculations estimated high picogram detection limits for a minor isomer coeluting with low to mid-nanogram quantity of a more abundant isomer. Further characterization of the analytes was performed using density functional theory computations to compare theory with experimental measurements. Additionally, gas chromatography – vacuum ultraviolet spectroscopy was shown to be able to speciate dimethylnaphthalenes in jet and diesel fuel samples.     

Covering and gluing of algebras and differential algebras

Extending work of Budzyński and Kondracki, we investigate coverings and gluings of algebras and differential algebras. We describe in detail the gluing of two quantum discs along their classical subspace, giving a C^*-algebra isomorphic to a certain Podleś sphere, as well as the gluing of U_q^1/2(sl₂)-covariant differential calculi on the discs.     

Extreme Covariant Observables for Type I Symmetry Groups

The structure of covariant observables—normalized positive operator measures (POMs)—is studied in the case of a type I symmetry group. Such measures are completely determined by kernels which are measurable fields of positive semidefinite sesquilinear forms. We produce the minimal Kolmogorov decompositions for the kernels and determine those which correspond to the extreme covariant observables. Illustrative examples of the extremals in the case of the Abelian symmetry group are given. Dedicated to Pekka J. Lahti in honor of his sixtieth birthday     

The Branch Processes of Chern-Simons (CS) <Emphasis Type="Italic">p</Emphasis>-Branes

In this paper, by making use of Duan’s topological current theory, the branch process of Chern-Simons (CS) p-branes is discussed in detail. Chern-Simons (CS) p-branes are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points and higher degenerated points systematically of the vector order parameter field . Furthermore, it is also shown that CS p-branes are found splitting or merging at the degenerate point of field function but the total topological charges of the CS p-branes are still unchanged.     

Point estimation for multi-spectral distributed random matrices

In this communication, we consider a p×n random matrix which is normally distributed with mean matrix M and covariance matrix Σ, where the multivariate observation x_i=y_i+?_i with p dimensions on an object consists of two components, the signal y_i with mean vector μ and covariance matrix Σ_s and noise with mean vector zero and covariance matrix Σ_?, then the covariance matrix of x_i and x_j is given by Σ=Cov(x_i,x_j)=Γ⊗(B_|i-j|Σ_s+C_|i-j|Σ_?), where Γ is a correlation matrix; B_|i-j| and C_|i-j| are diagonal constant matrices. The statistical objective is to consider the maximum likelihood estimate of the mean matrix M and various components of the covariance matrix Σ as well as their statistical properties, that is the point estimates of Σ_s,Σ_? and Γ. More importantly, some properties of these estimators are investigated in slightly more general models.     

半相依模型参数估计的改进

对于m个半相依回归系统的未知回归系数, 文献[7]提出一种利用信息逐次迭加的方法, 该文首先在其基础上给出一种进一步改进形式, 并得到了其相合性, 同时作者借鉴文献[7]提出逐次迭加信息的构造估计思想给出一种具有小样本优良性的可行估计, 模拟研究也表明作者的改进估计是有效的.文献[10]根据Rao的协方差改进思想, 给出一种更为简洁的两步估计, 该文在此估计基础上给出一种改进形式, 新估计具有更好的可操作性和均方误差意义下的优良性.     

比较法测试不同颜色匹配函数的性能

为了测试不同颜色匹配函数的预测性能,基于灰色、棕色、紫色和蓝色4个目标色,共制作了16对近同色异谱色样对(围绕每个目标色分别制作了4个待比较色),组织14名年龄不同的色觉正常观察者基于心理物理实验方法中的比较法,开展了色差大小比较实验。结果表明,实验组织的老年观察者的锥细胞响应较年轻观察者有所下降,CIE1931的预测性能优于CIE1964。不同颜色区域,各颜色匹配函数的表现各异,在进行某些颜色(如灰色,紫色和蓝色)区域的色度值表征和色差评估时,即便观察视场角大于4°,CIE1931的计算性能仍然优于CIE1964。现有CIE2006匹配函数考虑到晶状体光谱透光率和中央凹的锥细胞光谱响应,下一步可继续强化中央凹锥细胞光谱响应,优化其计算性能。     

Improved Estimation of Parameter Matrices in a One-Sample and Two-Sample Problems

In this paper, the problems of estimating the covariance matrix in a Wishart distribution (refer as one-sample problem) and the scale matrix in a multi-variate F distribution (which arise naturally from a two-sample setting) are considered. A new class of estimators which shrink the eigenvalues towards their harmonic mean is proposed. It is shown that the new estimator dominates the best linear estimator under two scale invariant loss functions.