Lognormal Approximations of Fault Tree Uncertainty Distributions

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed‐form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling‐based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed‐form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks’s method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models.     

Moderate Deviations for Bayes Posteriors

Let ( X_k ) k be a sequence of i.i.d. random variables taking values in a set , and consider the problem of estimating the law of X₁ in a Bayesian framework. We prove, under mild conditions on the prior, that the sequence of posterior distributions satisfies a moderate deviation principle.     

Statistical and Combinatorial Aspects of Comparative Genomics*

Abstract. This document presents a survey of the statistical and combinatorial aspects of four areas of comparative genomics: gene order based measures of evolutionary distances between species, construction of phylogenetic trees, detection of horizontal transfer of genes, and detection of ancient whole genome duplications.     

商业银行贷款定价模型构造研究

本文从贷款定价的原则和因素分析着手 ,提出贷款价格由核心价格、风险附加价格和可折让价格三部分组成 ,并建立了贷款定价数学模型。同时 ,利用决策树实现了贷款定价决策。     

一种基于神经网络和决策树的信用评估新方法

分析了数据挖掘在国内外金融领域的应用及研究现状,提出了一种基于神经网络和决策树相结合的信用评估新方法。该方法通过RBF神经网络,进行条件属性裁减,并利用决策树抽取出评估规则。此方法利用神经网络的“黑箱”工作特性,选择重要条件属性,并利用决策树自动生成评估规则,大大提高了信用评估的效率和客观性。     

Tree health mapping with multispectral remote sensing data at UC Davis, California

Tree health is a critical parameter for evaluating urban ecosystem health and sustainability. Traditionally, this parameter has been derived from field surveys. We used multispectral remote sensing data and GIS techniques to determine tree health at the University of California, Davis. The study area (363 ha) contained 8,962 trees of 215 species. Tree health conditions were mapped for each physiognomic type at two scales: pixel and whole tree. At the pixel scale, each tree pixel within the tree crown was classified as either healthy or unhealthy based on vegetation index values. At the whole tree scale, raster based statistical analysis was used to calculate tree health index which is the ratio of healthy pixels to entire tree pixels within the tree crown. The tree was classified as healthy if the index was greater than 70%. Accuracy was checked against a random sample of 1,186 trees. At the whole tree level, 86% of campus trees were classified as healthy with 88% mapping accuracy. At the pixel level, 86% of the campus tree cover was classified as healthy. This tree health evaluation approach allows managers to identify the location of unhealthy trees for further diagnosis and treatment. It can be used to track the spread of disease and monitor seasonal or annual changes in tree health. Also, it provides tree health information that is fundamental to modeling and analysis of the environmental, social, and economic services produced by urban forests.     

A circular-cone test for testing homogeneity against a simple tree order

Several methods exist for the problem of testing the equality of several treatments against the one-sided alternative that the treatments are better than the control. These methods include Dunnett's test, Bartholomew's likelihood-ratio test, the Abelson-Tukey-Schaafsma-Smid optimal-contrast test, and the multiple-contrast test of Mukerjee, Robertson, and Wright. A new test is proposed based on an approximation of the likelihood-ratio test of Bartholomew. This test involves using a circular cone in place of the alternative-hypothesis cone. The circular-cone test has excellent power characteristics similar to those of Bartholomew's test. Moreover, it has the advantages of being simpler to compute and may be used with unequal sample sizes.     

三叉判定树与伪币问题

对伪币问题提出了三叉判定树方法,并在计算机上给予验证。     

A fast splitting procedure for classification trees

This paper provides a faster method to find the best split at each node when using the CART methodology. The predictability index is proposed as a splitting rule for growing the same classification tree as CART does when using the Gini index of heterogeneity as an impurity measure. A theorem is introduced to show a new property of the index : the for a given predictor has a value not lower than the for any split generated by the predictor. This property is used to make a substantial saving in the time required to generate a classification tree. Three simulation studies are presented in order to show the computational gain in terms of both the number of splits analysed at each node and the CPU time. The proposed splitting algorithm can prove computational efficiency in real data sets as shown in an example.     

The web proxy location problem in general tree of rings networks

The Web proxy location problem in general networks is an NP-hard problem. In this paper, we study the problem in networks showing a general tree of rings topology. We improve the results of the tree case in literature and get an exact algorithm with time complexity O(nhk), where n is the number of nodes in the tree, h is the height of the tree (the server is in the root of the tree), and k is the number of web proxies to be placed in the net. For the case of networks with a general tree of rings topology we present an exact algorithm with O(kn ²) time complexity.This research has been supported by NSF of China (No. 10371028) and the Educational Department grant of Zhejiang Province (No. 20030622).