基于新安江模型的降雨不确定性传播

基于模糊隶属度理论,结合蒙特卡罗方法,定量分析了降雨不确定性在新安江模型中的传播特性及其对流量过程的影响。用模糊隶属度函数表示降雨量的不确定性,用蒙特卡罗方法把3 h雨量随机解集为1 h数据,以表征降雨时程分布的不确定性影响。应用新安江模型对褒河流域进行径流模拟。结果表明,雨量量级大小的不确定性在降雨不确定性中占据主导位置,降雨时程分布的影响次之。     

基于最优抽样与选择性解析的电力系统可靠性评估

为降低Monte Carlo法的计算方差,加快电力系统可靠性评估的速度,提出一种基于最优抽样和选择性解析的混合算法。该算法是在传统Monte Carlo法的基础上,增加小样本预抽样计算,以获得最优抽样密度函数与各变量的投影方差。根据投影方差的大小,确定解析变量,进行解析化处理,对模拟变量按照最优抽样密度函数抽取元件状态。对测试系统IEEE-RTS的算例分析表明,该算法可以同时提高抽样计算和解析计算的效率,降低计算方差,加快可靠性评估的速度。     

基于熵权的集对分析模型在水质综合评价中的应用

针对水质评价中各评价指标的不确定性,将集对分析理论应用于水质综合评价中。先通过计算评价样本与评价指标之间的联系度对样本做初步分类,再对样本做进一步的同一、差异、对立的集对分析以判断评价样本的等级。在确定各评价指标的权重时,将信息论中的熵值理论引入该模型,运用信息熵所反映实测数据的效用值计算各评价指标的权重,使权重的分配具有一定的理论依据。最后运用蒙特卡罗法构造算例,讨论了实测过程中的随机观测误差对评价结果的影响。经实例分析,通过与综合评判法、属性识别法和模糊物元法的比较表明,基于熵权的集对分析模型的评价结果合理、客观。     

致灾因素耦合作用下堆积体斜坡失稳概率研究

藏东南地区气候环境复杂,地质条件恶劣,广为分布的堆积体斜坡易在多种极端条件诱发下失稳,具有较大的潜在风险。为研究复杂环境条件对滑坡的诱发作用,提出一种能够考虑多种诱发因素耦合作用的滑坡危险性评价方法。以地震和降雨为例,分别考虑了诱发因素自身的随机性与诱发作用的不确定性,通过分析不同危险性量级诱发事件的发生概率与回归周期,结合蒙特卡罗模拟计算对应诱发作用下的斜坡失稳概率,揭示不同程度的危险性序列。在此基础上利用全概率公式进行多致灾因素的耦合计算,系统评价堆积体斜坡的危险性与潜在风险。并以川藏交通廊道沿线某典型堆积体斜坡为算例,其结果表明:耦合计算结果为中等危险等级,总的规律表现为诱发事件组合越极端,其综合危险性反而越低。     

基于蒙特卡罗法的缓变型防洪风险分析

针对水库大坝服役期的水文、水力不确定性因素及工程结构风险等因素的影响,在时变效应理论的基础上,构建了时变随机变量量化的函数模型,并提出缓变型防洪风险分析模型;同时运用蒙特卡罗法(Monte Carlo method)来求解风险率,进而定量的分析大坝的防洪安全。以池潭水电站为例,利用监测资料序列构建坝前最高水位与坝顶高程的缓变历程的函数关系,结果分析表明:大坝继续使用期内的防洪风险率满足现行规范设防标准,可为大坝的防洪风险评估提供科学依据,亦可将该分析方法拓展至其他服役水利工程的防洪安全评估。     

水工钢闸门主梁模糊失效概率计算方法研究

为合理计算水工钢闸门主梁模糊失效概率,分别将主梁相对变形当作一个随机变量及三个变量的组合,采用积分法、当量随机化方法及蒙特卡罗法进行了计算。当相对变形为一个随机量时,采用积分法及当量随机化方法计算,两者的差别在于积分法用隶属函数描述模糊限值,当量随机化方法是将模糊限值当量作为一个随机量。当相对变形看作三个变量的组合时采用蒙特卡罗法进行计算,该方法考虑了三个变量的分布特性,更符合实际情况,模糊限值也用随机量表示。计算表明,积分法与当量随机化方法结果相近,验证了当量随机化方法的精度;蒙特卡罗法结果与相对变形服从正态分布时、用当量随机化方法计算的结果接近,故主梁相对变形服从正态分布更为合理。三种计算方法中,当量随机化方法计算失效概率相较于其它方法有计算过程简便,效率高的优点。     

Scaledt分布、杠杆效应和上证综指的VaR风险

与正态分布相比,上证指数收益率的经验分布具有尖峰厚尾特征,但用Scaled t-分布比正态分布可以更好地拟合上证指数收益率的经验分布。本文以Scaled t-分布假设下的GJR模型为基础,测量了上证指数收益率波动性的杠杆效应,即信息对波动性的不对称影响：并根据GJR模型应用Monte Carlo模拟方法,测定上证指数日收益率和持有期收益率的风险价值（VaR）。根据GJR模型提供的结果,上证指数30天、60天和90天持有期收益率的风险值分别为12．1％、17．8％、22．0％。用GJR模型比均值-方差模型和历史模拟方法计算的5％显著性水平VaR值更接近实际收益率。     

MC's for MCMC'ists

We develop a minimum amount of theory of Markov chains at as low a level of abstraction as possible in order to prove two fundamental probability laws for standard Markov chain Monte Carlo algorithms:
1. The law of large numbers explains why the algorithm works: it states that the empirical means calculated from the samples converge towards their "true" expected values, viz. expectations with respect to the invariant distribution of the associated Markov chain (=the target distribution of the simulation).
2. The central limit theorem expresses the deviations of the empirical means from their expected values in terms of asymptotically normally distributed random variables. We also present a formula and an estimator for the associated variance.     

Predicting Variability in a Lake Ontario Phosphorus Model

The prediction of a model always has a degree of uncertainty. Because the level of uncertainty is inversely related to the value of information contained in the prediction, there is a need to quantify the uncertainty. One approach to estimate prediction uncertainty is first-order error analysis. In this method, the error in a characteristic (variable or parameter) is defined by its first nonzero moment (the variance). Errors are propagated through the model using first-order terms in the Taylor series, and the variances are then combined to yield the total prediction uncertainty. An alternative approach to model prediction error analysis is Monte Carlo simulation. In this technique, probability density functions are assigned to each characteristic (variable or parameter), reflecting the uncertainty in that characteristic. Then, values are randomly selected from the distribution for each term and inserted into the model, to calculate a prediction. Repeating this process a number of times produces a distribution of predicted values, which reflects the combined uncertainties. These two approaches (first-order error analysis and Monte Carlo simulation) are applied to Lake Ontario data using a steady state mass balance phosphorus model. Comparisons are made which suggest guidelines for the use of each.     

On the Application of Markov Chain Monte Carlo Methods to Genetic Analyses on Complex Pedigrees

Markov chain Monte Carlo methods are frequently used in the analyses of genetic data on pedigrees for the estimation of probabilities and likelihoods which cannot be calculated by existing exact methods. In the case of discrete data, the underlying Markov chain may be reducible and care must be taken to ensure that reliable estimates are obtained. Potential reducibility thus has implications for the analysis of the mixed inheritance model, for example, where genetic variation is assumed to be due to one single locus of large effect and many loci each with a small effect. Similarly, reducibility arises in the detection of quantitative trait loci from incomplete discrete marker data. This paper aims to describe the estimation problem in terms of simple discrete genetic models and the single-site Gibbs sampler. Reducibility of the Gibbs sampler is discussed and some current methods for circumventing the problem outlined.