Stability Relationships Among the Gibbs Sampler and its Subchains

The use of Gibbs samplers driven by improper posteriors has been a controversial issue in the statistics literature over the last few years. It has recently been demonstrated that it is possible to make valid statistical inferences through such Gibbs samplers. Furthermore, theoretical and empirical evidence has been given to support the idea that there are actually computational advantages to using these nonpositive recurrent Markov chains rather than more standard positive recurrent chains. These results provide motivation for a general study of the behavior of the Gibbs Markov chain when it is not positive recurrent. This article concerns stability relationships among the two-variable Gibbs sampler and its subchains. We show that these three Markov chains always share the same stability; that is, they are either all positive recurrent, all null recurrent, or all transient. In addition, we establish general results concerning the ways in which positive recurrent Markov chains can arise from null recurrent and transient Gibbs chains. Six examples of varying complexity are used to illustrate the results.     

JavaStatSoft: design patterns and features

JavaStatSoft, implemented using Java, is an open-source software for performing statistics. The current features of JavaStatSoft are described. Several well-known patterns the software used are introduced. In addition, based on these patterns and the experience in developing the software, a new framework, referred to as Data Analysis Module, is proposed to help programmers develop a user-friendly software for data analysis.     

Une méthode inverse d'ordre un pour les problèmes de complétion de données

An iterative resolution method for inverse Cauchy problems is presented. The successive iterations satisfy the equilibrium equations exactly. Numerical simulations prove the accuracy of the method and its ability to solve Cauchy problems when the domain boundary is not regular. To cite this article: A. Cimetière et al., C. R. Mecanique 333 (2005).     

Covering symmetric semi-monotone functions

We define a new set of functions called semi-monotone, a subclass of skew-supermodular functions. We show that the problem of augmenting a given graph to cover a symmetric semi-monotone function is NP-complete if all the values of the function are in {0,1} and we provide a minimax theorem if all the values of the function are different from 1. Our problem is equivalent to the node to area augmentation problem. Our contribution is to provide a significantly simpler and shorter proof.     

Combined neural network and reduced FRF techniques for slight damage detection using measured response data

Summary  This paper deals with structural damage detection using measured frequency response functions (FRF) as input data to artificial neural networks (ANN). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a data-reduction technique based on principal component analysis (PCA). The compressed FRFs, represented by their projection onto the most significant principal components, were used as the ANN input variables instead of the raw FRF data. The output is a prediction of the actual state of the specimen, i.e. healthy or damaged. A further advantage of this particular approach is its ability to deal with relatively high measurement noise, which is a common occurrence when dealing with industrial structures. The methodology was applied to detect three different states of a space antenna: reference, slight mass damage and slight stiffness damage. About 600 FRF measurements, each with 1024 spectral points, were included in the analysis. Six 2-hidden layer networks, each with an individually-optimised architecture for a specific FRF reduction level, were used for damage detection. The results showed that it was possible to distinguish between the three states of the antenna with good accuracy, subject to using an adequate number of principal components together with a suitable neural network configuration. It was also found that the quality of the raw FRF data remained a major consideration, though the method was able to filter out some of the measurement noise. The convergence and detection properties of the networks were improved significantly by removing those FRFs associated with measurement errors. Received 9 March 2000; accepted for publication 12 December 2000     

Size of random Galois lattices and number of closed frequent itemsets

Given a sample of binary random vectors with i.i.d. Bernoulli(p) components, that is equal to 1 (resp. 0) with probability p (resp. 1−p), we first establish a formula for the mean of the size of the random Galois lattice built from this sample, and a more complex one for its variance. Then, noticing that closed α-frequent itemsets are in bijection with closed α-winning coalitions, we establish similar formulas for the mean and the variance of the number of closed α-frequent itemsets. This can be interesting for the study of the complexity of some data mining problems such as association rule mining, sequential pattern mining and classification.     

Reputation and efficiency: A non-parametric assessment of America’s top-rated MBA programs

Widely publicized reports of fresh MBAs getting multiple job offers with six-figure annual salaries leave a long-lasting general impression about the high quality of selected business schools. While such spectacular achievement in job placement rightly deserves recognition, one should not lose sight of the resources expended in order to accomplish this result. In this study, we employ a measure of Pareto-Koopmans global efficiency to evaluate the efficiency levels of the MBA programs in Business Week’s top-rated list. We compute input- and output-oriented radial and non-radial efficiency measures for comparison. Among three tier groups, the schools from a higher tier group on average are more efficient than those from lower tiers, although variations in efficiency levels do occur within the same tier, which exist over different measures of efficiency.     

不精确数据的相似度及其在聚类分析中的应用

基本包含度理论，提出不精确数据的一种相似度，并讨论基于此相似度的不精确数据的聚类方法。