Nonparametric Bayesian Modeling for Stochastic Order

In comparing two populations, sometimes a model incorporating stochastic order is desired. Customarily, such modeling is done parametrically. The objective of this paper is to formulate nonparametric (possibly semiparametric) stochastic order specifications providing richer, more flexible modeling. We adopt a fully Bayesian approach using Dirichlet process mixing. An attractive feature of the Bayesian approach is that full inference is available regarding the population distributions. Prior information can conveniently be incorporated. Also, prior stochastic order is preserved to the posterior analysis. Apart from the two sample setting, the approach handles the matched pairs problem, the k-sample slippage problem, ordered ANOVA and ordered regression models. We illustrate by comparing two rather small samples, one of diabetic men, the other of diabetic women. Measurements are of androstenedione levels. Males are anticipated to produce levels which will tend to be higher than those of females.     

Language Constructs for Modeling Stochastic Linear Programs

This paper introduces two tokens of syntax for algebraic modeling languages that are sufficient to model a wide variety of stochastic optimization problems. The tokens are used to declare random parameters and to define a precedence relationship between different random events. It is necessary to make a number of assumptions in order to use this syntax, and it is through these assumptions, which cover the areas of model structure, time, replication, and stages, that we can attain a deeper understanding of this class of problem.     

Asymptotics for Statistical Distances Based on Voronoi Tessellations

We obtain an information-type inequality and a strong law for a wide class of statistical distances between empirical estimates and random measures based on Voronoi tessellations. This extends some basic results in the asymptotic theory of sample spacings, when the cells of the Voronoi tessellation are interpreted as d-dimensional spacings.     

随机调幅Rattling系统建模

本文研究了一个随机调幅Ｒａｔｌｉｎｇ系统·代替常用的数值分析方法,采用非高斯截断技术,导出一个由三维平均映射描述的离散的随机模型·实测指出该模型能揭示浑沌随机性质,故更适于用以模拟齿轮箱噪声源     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

Convergence of a Stochastic Method for the Modeling of Polymeric Fluids

We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.     

气温随机模型与我国气温期权定价研究

建立气温期权交易对于对冲天气风险,增加市场金融投资品种具有重要意义。本文主要参照均值回复模型,考虑气温的季节变化和长期趋势,建立反映气温变化的随机模型,应用1980至1999年北京日平均气温对模型参数进行估计。实证仿真以及模型验证结果表明,模型的相对误差较小,建立的气温随机模型能够对未来气温变化进行较好的模拟。蒙特卡罗方法能够对天气衍生产品进行合理定价。     

The Combinatorial Structure of Spatial STIT Tessellations

Spatially homogeneous random tessellations that are stable under iteration (nesting) in the $3$ 3 -dimensional Euclidean space are considered, so-called STIT tessellations. They arise as outcome of a space-time process of subsequent cell division and, consequently, they are not facet-to-facet. The intent of this paper is to develop a detailed analysis of the combinatorial structure of such tessellations and to determine a number of new geometric mean values, for example for the neighbourhood of the typical vertex. The heart of the results is a fine classification of tessellation edges based on the type of their endpoints or on the equality relationship with other types of line segments. In the background of the proofs are delicate distributional properties of spatial STIT tessellations.     

基于MCMC模拟的贝叶斯厚尾金融随机波动模型分析

针对现有金融时间序列模型建模方法难以刻画模型参数的渐变性问题,利用贝叶斯分析方法构建贝叶斯厚尾SV模型。首先对反映波动性特征的厚尾金融随机波动模型(SV-T)进行贝叶斯分析,构造了基于Gibbs抽样的MCMC数值计算过程进行仿真分析,并利用DIC准则对SV-N模型和SV-T模型进行优劣比较。研究结果表明:在模拟我国股市的波动性方面,SV-T模型比SV-N模型更优,更能反应我国股市的尖峰厚尾的特性,并且证明了我国股市具有很强的波动持续性。     

Asymptotic Shapes of large Cells in Random Tessellations

We establish a close relationship between isoperimetric inequalities for convex bodies and asymptotic shapes of large random polytopes, which arise as cells in certain random mosaics in d-dimensional Euclidean space. These mosaics are generated by Poisson hyperplane processes satisfying a few natural assumptions (not necessarily stationarity or isotropy). The size of large cells is measured by a class of general functionals. The main result implies that the asymptotic shapes of large cells are completely determined by the extremal bodies of an inequality of isoperimetric type, which connects the size functional and the expected number of hyperplanes of the generating process hitting a given convex body. We obtain exponential estimates for the conditional probability of large deviations of zero cells from asymptotic or limit shapes, under the condition that the cells have large size. This work was supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953. Received: May 2005 Accepted: September 2005     

Advances in Studies and Applications of Centroidal Voronoi Tessellations

<正>Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating.     

Automatic Formulation of Stochastic Programs Via an Algebraic Modeling Language

This paper presents an open source tool that automatically generates the so-called deterministic equivalent in stochastic programming. The tool is based on the algebraic modeling language ampl. The user is only required to provide the deterministic version of the stochastic problem and the information on the stochastic process, either as scenarios or as a transitions-based event tree.     

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specifies the probability distribution of its corresponding random variable. Our goal in this work is to lay the foundations of the innovation model, a (possibly) non-Gaussian probabilistic model for sparse signals. This is achieved by using the characteristic functional to specify sparse stochastic processes that are defined as linear transformations of general continuous-domain white Lévy noises (also called innovation processes). We prove the existence of a broad class of sparse processes by using the Minlos–Bochner theorem. This requires a careful study of the regularity properties, especially the \(L^p\) -boundedness, of the characteristic functional of the innovations. We are especially interested in the functionals that are only defined for \(p<1\) since they appear to be associated with the sparser kind of processes. Finally, we apply our main theorem of existence to two specific subclasses of processes with specific invariance properties.     

案例教学在《应用随机过程》中的探索和实践

通过C-K方程在推断系统发育树中的应用的角度对案例教学法进行了探索和实践,并在此基础上对应用随机过程的教学进行了几点粗略的探讨.