Bayesian source detection and parameter estimation of a plume model based on sensor network measurements

We consider a network of sensors that measure the intensities of a complex plume composed of multiple absorption–diffusion source components. We address the problem of estimating the plume parameters, including the spatial and temporal source origins and the parameters of the diffusion model for each source, based on a sequence of sensor measurements. The approach not only leads to multiple‐source detection, but also the characterization and prediction of the combined plume in space and time. The parameter estimation is formulated as a Bayesian inference problem, and the solution is obtained using a Markov chain Monte Carlo algorithm. The approach is applied to a simulation study, which shows that an accurate parameter estimation is achievable. Copyright © 2010 John Wiley & Sons, Ltd.     

The writhe of permutations and random framed knots

We introduce and study the writhe of a permutation, a circular variant of the well‐known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non‐Gaussian limit distribution. This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model, studied with Hass, Linial, and Nowik (Discrete Comput Geom, 2016). The distribution of the framing in this model is equivalent to the writhe of random permutations. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 121–142, 2017     

Path Boxplots: A Method for Characterizing Uncertainty in Path Ensembles on a Graph

Graphs are powerful and versatile data structures that can be used to represent a wide range of different types of information. In this article, we introduce a method to analyze and then visualize an important class of data described over a graph—namely, ensembles of paths. Analysis of such path ensembles is useful in a variety of applications, in diverse fields such as transportation, computer networks, and molecular dynamics. The proposed method generalizes the concept of band depth to an ensemble of paths on a graph, which provides a center-outward ordering on the paths. This ordering is, in turn, used to construct a generalization of the conventional boxplot or whisker plot, called a path boxplot, which applies to paths on a graph. The utility of path boxplot is demonstrated for several examples of path ensembles including paths defined over computer networks and roads. Supplementary materials for this article are available online.     

离散型最小和最大次序统计量相关性研究

本文研究离散型随机变量之间的相关性度量, 讨论了最小次序统计量和最大次序统计量的渐近独立性, 给出了计算最小次序统计量和最大次序统计量的Kendall和Spearman秩相关系数的公式.     

Confidence intervals in the solution of stochastic integer linear programming problems

A method is proposed to estimate confidence intervals for the solution of integer linear programming (ILP) problems where the technological coefficients matrix and the resource vector are made up of random variables whose distribution laws are unknown and only a sample of their values is available. This method, based on the theory of order statistics, only requires knowledge of the solution of the relaxed integer linear programming (RILP) problems which correspond to the sampled random parameters. The confidence intervals obtained in this way have proved to be more accurate than those estimated by the current methods which use the integer solutions of the sampled ILP problems.This research was partially supported by the Italian National Research Council contract no. 82.001 14.93 (P.F. Trasporti).     

Sparse Steinian Covariance Estimation

We consider a new method for sparse covariance matrix estimation which is motivated by previous results for the so-called Stein-type estimators. Stein proposed a method for regularizing the sample covariance matrix by shrinking together the eigenvalues; the amount of shrinkage is chosen to minimize an unbiased estimate of the risk (UBEOR) under the entropy loss function. The resulting estimator has been shown in simulations to yield significant risk reductions over the maximum likelihood estimator. Our method extends the UBEOR minimization problem by adding an ?₁ penalty on the entries of the estimated covariance matrix, which encourages a sparse estimate. For a multivariate Gaussian distribution, zeros in the covariance matrix correspond to marginal independences between variables. Unlike the ?₁-penalized Gaussian likelihood function, our penalized UBEOR objective is convex and can be minimized via a simple block coordinate descent procedure. We demonstrate via numerical simulations and an analysis of microarray data from breast cancer patients that our proposed method generally outperforms other methods for sparse covariance matrix estimation and can be computed efficiently even in high dimensions.     

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??In this paper, we compare the smallest order statistics arising from multiple-outlier models when the numbers of independent and identically distributed random variables are different. Let and denote the smallest order statistics among, and, respectively, whereand. We then prove that $ and are ordered in terms of the usual stochastic order, hazard rate order and likelihood ratio order under the majorization relationship between and.     

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In this paper, we study the stochastic comparisons of order statistics from generalized normal distributions. We obtain some sufficient conditions for ordering results based on parameter matrix and vector majorization comparisons. These conditions are necessary in some cases.     

基于成分统计的我国人口年龄构成变动分析

人口年龄构成是总人口自然素质的重要表现因素,它不仅关系到人口自身的发展问题,同时也会对社会经济发展产生重大的影响。本文根据1990-2006期间的人口分性别年龄普查和抽样调查资料,对这一时期我国人口年龄构成及其变动情况进行了分析。主要内容包括:男性人口年龄构成变动的描述性分析,女性人口年龄构成变动的描述性分析,男性人口年龄构成与女性人口年龄构成的对比和检验等。     

概率统计课程教学方法的几点体会

通过教学实践与理论思考,并结合目前大学生的特点,对概率论与数理统计课程的教学方法阐述四点看法.主张在教学中引人历史典故,引进多媒体辅助教学,将教学与数学建模活动相结合,运用案例教学法以培养学生分析问题和解决问题的能力.