The Quadratic Collision Probability Method and the Importance Sampling Method in Monte Carlo Calculation for the Flux at a Point

The unbounded estimate is one of the troublesome problems in Monte Carlo method. Particularly, in the calculation for the flux at a point, the estimate may approach infinite. In this paper, a collision probability method is proposed in Monte Carlo calculation for the flux at a point, and two kinds of methods with the bounded estimation are presented: the quadratic collision probability method and the importance sampling method. The former method is simple and easy to use, whereas the latter is suitable for calculation of flux at many different points simultaneously. The practical calculation indicates that the variance of the present methods can be reduced by about 50% and the efficiency can be increased by 2 to 4 time in comparison with the existing methods.     

Time-Dependent Marginal Energy Costs in Power Systems with Forced Outages

Marginal pricing of electricity calls for the determination of marginal energy costs over time. The purpose of this paper is to provide a computationally efficient procedure for computing the time-dependent probability, under merit order operation and forced outages of units, that any given plant will be the last plant used in a given multi-plant power system. This then allows a straightforward calculation of expected marginal energy cost for the given-power system over time. Other performance measures are derived as a by-product at relatively little extra computational effort. The method is applied to a realistic system and numerical results are presented and discussed.     

Calculation of Optimal Bounds on the Probability of Failure of Soft Biological Tissues

In this contribution, a methodology for the calculation of optimal bounds on the probability of failure of soft biological tissues is presented. Two potential rupture criteria are considered and an uncertainty quantification method [1] is applied to a virtual experimental data set. The results for both criteria are compared in a finite element example. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite-time ruin probability in the inhomogeneous claim case

This paper deals with the discrete-time risk model with nonidentically distributed claims. The recursive formula of finite-time ruin probability is obtained, which enables one to evaluate the probability of ruin with desired accuracy. Rational valued claims and nonconstant premium payments are considered. Some numerical examples of finite-time ruin probability calculation are presented.     

结构的失效可能度及模糊概率计算方法

依据模糊可能性理论,系统地建立含模糊变量时结构的可靠性计算模型。旨在解决模糊结构、模糊-随机结构和模糊状态假设下结构的可靠性计算问题。所建模型可给出模糊结构失效的可能度和模糊-随机结构失效概率的可能性分布。研究表明:对同时含模糊变量和随机变量的混合可靠性计算问题,把失效概率(或可靠度)作为模糊变量,能更客观地反映系统的安全状况。算例分析说明了文中方法的合理性和有效性。     

概率计算中易混淆问题的教法研究

首先从具体实例提出了物品检验概率计算中一类易混淆问题.然后从理论上证明了无放回逐次抽取中两种概率计算方法的合理性,其定理证明过程充分揭示了这类检验方法与其它相关抽取方式之间的关系并强调了最根本的分析问题思路.最后,研究了文中所得到的一般性结论的适用范围,从而使得这类易混淆问题的讲解变得清晰条理.     

From characteristic function to distribution function via fourier analysis

In this paper characteristic functions of probability distributions are considered. The numerical calculation of the distribution function when the characteristic function is known is discussed and two different methods are presented.     

判别分析在基因剪切位点识别中的应用

基因的结构预测是目前极为活跃的研究领域,而基因剪切位点的识别则是基因结构预测中的重要环节.本文采用自己提出的平均似然比等方法,同时采用目前较为有效的权重矩阵(WMM)、最大相关分解(MDD)、动态规划等模型,充分提取剪切位点信号区的统计特征,采用统计中判别分析的方法进行判别,得到了较好的判别效果,并与其它方法进行了比较.     

Numerical Computation of Multivariate Normal Probabilities

Abstract

The numerical computation of a multivariate normal probability is often a difficult problem. This article describes a transformation that simplifies the problem and places it into a form that allows efficient calculation using standard numerical multiple integration algorithms. Test results are presented that compare implementations of two algorithms that use the transformation with currently available software.     

M/M/c休假排队系统稳态分布的数值计算

从数值计算角度研究M/M/c休假排队系统稳定状态的概率分布.采用GMRES方法求解概率分布向量所满足的大型线性方程,构造了一个循环预处理算子加速GMRES方法的收敛.数值实例验证了该算法的优越性.     

On numerical calculation of probabilities according to Dirichlet distribution

The main difficulty in numerical solution of probabilistic constrained stochastic programming problems is the calculation of the probability values according to the underlying multivariate probability distribution. In addition, when we are using a nonlinear programming algorithm for the solution of the problem, the calculation of the first and second order partial derivatives may also be necessary.     

On the stochastic optimization problems of plastic metal working processes under stochastic initial conditions

The article is devoted to mathematical modeling of problems of stochastic optimization of the plastic metal working. Classification and mathematical statements of such problems are proposed. Several calculation techniques of the single goal function are presented. The probability theory and the Fuzzy Numbers were applied for solution of the problems of stochastic optimization.     

Extended rough set model based on known same probability dominant valued tolerance relation

Classical rough set theory is based on the conventional indiscernibility relation. It is not suitable for analyzing incomplete information. Some successful extended rough set models based on different non-equivalence relations have been proposed. The data-driven valued tolerance relation is such a non-equivalence relation. However, the calculation method of tolerance degree has some limitations. In this paper, known same probability dominant valued tolerance relation is proposed to solve this problem. On this basis, an extended rough set model based on known same probability dominant valued tolerance relation is presented. Some properties of the new model are analyzed. In order to compare the classification performance of different generalized indiscernibility relations, based on the category utility function in cluster analysis, an incomplete category utility function is proposed, which can measure the classification performance of different generalized indiscernibility relations effectively. Experimental results show that the known same probability dominant valued tolerance relation can get better classification results than other generalized indiscernibility relations.     

C&T条件下碳排放核查三方博弈研究

针对总量控制与交易机制(C&T)条件下的碳排放核查问题,构建了一个三方博弈模型,对控排企业、第三方核查机构和政府监管部门的博弈行为进行了分析,得到了该三方博弈的均衡条件;对于当前给定政府复查行为,分析了企业的最优上报碳强度。研究结果表明,“以历史碳强度为参考,控排企业上报碳强度差异越大复查概率越大”的政府复查机制存在一定的不合理性,尤其当实际碳强度高于参考碳强度时,可能导致控排企业和第三方核查机构的合谋;相对配额分配方式下,碳强度上升比总排放上升更可能导致控排企业瞒报碳排放,而且工业增加值高的大企业瞒报风险更高;当政府复查概率提高到一定程度时,可以有效抑制控排企业和第三方核查机构的合谋行为。本文的研究结果对政府碳排放复查政策的制定具有一定的借鉴意义。     

Polynomial Approximations for Bivariate Aggregate Claims Amount Probability Distributions

A numerical method to compute bivariate probability distributions from their Laplace transforms is presented. The method consists in an orthogonal projection of the probability density function with respect to a probability measure that belongs to a Natural Exponential Family with Quadratic Variance Function (NEF-QVF). A particular link to Lancaster probabilities is highlighted. The procedure allows a quick and accurate calculation of probabilities of interest and does not require strong coding skills. Numerical illustrations and comparisons with other methods are provided. This work is motivated by actuarial applications. We aim at recovering the joint distribution of two aggregate claims amounts associated with two insurance policy portfolios that are closely related, and at computing survival functions for reinsurance losses in presence of two non-proportional reinsurance treaties.     

关于概率中样本空间选取的两点体会

从古典概型中事件概率的计算和事件的相互独立性两个方面,通过举例较深入地分析了样本空间选取的重要性,并指出在概率计算中要充分利用概率概念.     

A survey of simulated annealing as a tool for single and multiobjective optimization

This paper presents a comprehensive review of simulated annealing (SA)-based optimization algorithms. SA-based algorithms solve single and multiobjective optimization problems, where a desired global minimum/maximum is hidden among many local minima/maxima. Three single objective optimization algorithms (SA, SA with tabu search and CSA) and five multiobjective optimization algorithms (SMOSA, UMOSA, PSA, WDMOSA and PDMOSA) based on SA have been presented. The algorithms are briefly discussed and are compared. The key step of SA is probability calculation, which involves building the annealing schedule. Annealing schedule is discussed briefly. Computational results and suggestions to improve the performance of SA-based multiobjective algorithms are presented. Finally, future research in the area of SA is suggested.     

有序分组资料的线性趋势检验的确切概率计算

有序分组资料的线性趋势检验主要用于检验几个二项总体反应率的线性趋势；在医学与生物学中最典型的用途是研究剂量和反应的关系． 如果用Ｚ检验来代替通常在本检验中所用的卡方检验，就可容易地导出本检验的确切概率计算方法，和其他２×Ｃ有序列联表有着相同的形式．本文给出了该检验的确切概率计算方法．     

Probability that a Sequence is Lost Without Trace Under the Neutral Wright–Fisher Model with Recombination

I describe an approximate formula for calculating the short-term probability of loss of a sequence under the neutral Wright–Fisher model with recombination. I also present an upper and lower bound for this probability. Exact analytical calculation of this quantity is difficult and computationally expensive because the number of different ways in which a sequence can be lost, grows very large in the presence of recombination. Simulations indicate that the probabilities obtained using my approximation are always comparable to the true expectations provided that the number of generations remains small. These results are useful in the context of an algorithm that we recently developed for simulating Wright–Fisher populations forward in time.     

基于信用利差与Logistic回归的公司违约概率测算模型与实证研究

用Logistic模型计算公司违约概率在实际应用中存在两个问题:一是在缺乏公司违约记录数据库或违约记录数据库不典型的情况下,无法应用该模型或模型计算结果不准确;二是现有Logistic违约概率模型忽视了不同行业财务指标分布特征的差异性,导致公司违约概率计算结果的准确性降低。针对问题一,本文通过公司债券信用利差计算市场隐含的公司违约概率,在Logistic变换的基础上进一步确定Logistic线性回归的参数,使得公司违约概率的计算结果符合债券市场的实际状况。针对问题二,通过不同行业关键财务指标的单因子方差分析,证实了行业间财务指标的分布特征具有显著性差异,通过拟合优度证实了区分行业建立Logistic违约概率模型可显著提高违约概率测算的准确性。本文Logistic违约概率模型的构建过程如下:通过初选财务指标的相关性分析,删除反映信息重复的财务指标;通过Logistic回归中财务指标系数的显著性检验,删除对违约概率解释能力弱的财务指标;以Logistic回归的拟合优度为标准,选取各样本行业Logistic违约概率模型的关键财务指标,建立了机械设备等5个样本行业的Logistic违约概率模型,为样本内行业公司违约概率的准确测算提供模型与方法。本文的创新与特色:一是在无套利条件下,通过公司债券信用利差计算市场隐含的公司违约概率,并对其进行Logistic变换,作为Logistic线性回归的被解释变量,解决了在缺乏公司违约记录数据情况下Logistic违约概率模型的参数估计问题;二是通过单因子方差分析方法,证实了行业间财务指标的分布特征具有显著性差异,说明应区分行业建立Logistic违约概率模型;三是通过财务指标间的相关分析删除反映信息重复的财务指标,通过财务指标系数的显著性检验删除对公司违约概率解释能力弱的财务指标,保证了Logistic违约概率模型中关键财务指标选取的合理性;四是实证研究结果表明,不同行业的Logistic违约概率模型的关键财务指标不同,同一财务指标的参数也存在显著差异。实证研究结果还表明,区分行业建立Logistic违约概率模型与不区分行业相比,前者可将拟合优度及调整后的拟合优度提高近1倍。本文研究结果对于提高公司违约概率测算的准确性具有重要参考意义,对于商业银行贷款定价、公司债券发行定价、银行信用风险管理具有重要参考意义。