An accurate program for radiation modelling in the desigh of high-tempersature furnaces

The zone method is well established for determining radiativeheat transfer. It has been used successfully in simple geometries.However the task of determining the required exchange areashas limited its use in more geometrically complex enclosures.In this paper, a computer program, RADEX, is descrilxd. Thisprogram will calculate direct and total exchange areas usinga Monte Carlo method for enclosures with complex geometries.Some results from a validation study of RADEX are given. Finally,as an illustration of its potency as a design tool, the resultsof a comparative study of nine different designs of radianttube furnace are given.     

Testing linearity against threshold effects: uniform inference in quantile regression

This paper develops a uniform test of linearity against threshold effects in the quantile regression framework. The test is based on the supremum of the Wald process over the space of quantile and threshold parameters. We establish the limiting null distribution of the test statistic for stationary weakly dependent processes, and propose a simulation method to approximate the critical values. The proposed simulation method makes the test easy to implement. Monte Carlo experiments show that the proposed test has good size and reasonable power against non-linear threshold models.     

正贡献蒙特卡罗方法

考虑不依赖时间的粒子输运问题.不妨碍一般性,还限定问题是与能量无关的.令P=(r,Ω),其中r和Ω分别表示粒子的位置和运动方向单位矢量.用S(P)表示粒子源;φ(P)表示粒子通量;D(P)表示探测器对粒子通量的响应函数.目的是要计算如下积分效应:     

On the numerical modelling of the transitional flow in rarefied gases

The aim of this work is to simulate rarefied gas flow in complex geometries, under flow conditions that range from the hydrodynamic, through the transitional, to the molecular regimes. Existing computational models apply to molecular or viscous flow, but the treatment of the transitional flow is still underdeveloped.To deal with the difficult transitional flow, two models with overlapping ranges of applicability are introduced. A direct simulation Monte Carlo (DSMC) type model, which can be used in the molecular and up to the lower transitional flow, has been designed. For the viscous to the upper transitional flow, a numerical model using a particle method is proposed. The objective is to obtain a smooth transition between the probabilistic simulation of particle histories and the deterministic approach of the solution of partial differential equations.The DSMC model has been successfully applied to molecular and lower transitional flow in a complex geometry with stationary and moving boundaries. The test results agree well with published data. The particle method was tested using simplified Navier-Stokes equations in a channel. Preliminary results in the low viscous range seem to indicate that the approach is viable.     

Computation of optimal portfolios using simulation-based dimension reduction

This paper describes a simple and efficient method for determining the optimal portfolio for a risk averse investor. The portfolio selection problem is of long standing interest to finance scholars and it has obvious practical relevance. In a complete market the modern procedure for computing the optimal portfolio weights is known as the martingale approach. Recently, alternative implementations of the martingale approach based on Monte Carlo methods have been proposed. These methods use Monte Carlo simulation to compute stochastic integrals. This paper examines the efficient implementation of one of these methods due to [Cvitanic, J., Goukasian, L., Zapatero, F. 2003. Monte Carlo computation of optimal portfolios in complete markets. J. Econom. Dynam. Control 27, 971-986]. We explain why a naive application of the quasi-Monte Carlo method to this problem is often only marginally more efficient than the classical Monte Carlo method. Using the dimension reduction technique of [Imai, J., Tan, K.S., 2007. A general dimension reduction method for derivative pricing. J. Comput. Financ. 10 (2), 129-155] it is possible to significantly reduce the effective dimension of the problem. The paper shows why the proposed technique leads to a dramatic improvement in efficiency.     

Computation of optimal portfolios using simulation-based dimension reduction

This paper describes a simple and efficient method for determining the optimal portfolio for a risk averse investor. The portfolio selection problem is of long standing interest to finance scholars and it has obvious practical relevance. In a complete market the modern procedure for computing the optimal portfolio weights is known as the martingale approach. Recently, alternative implementations of the martingale approach based on Monte Carlo methods have been proposed. These methods use Monte Carlo simulation to compute stochastic integrals. This paper examines the efficient implementation of one of these methods due to [Cvitanic, J., Goukasian, L., Zapatero, F. 2003. Monte Carlo computation of optimal portfolios in complete markets. J. Econom. Dynam. Control 27, 971–986]. We explain why a naive application of the quasi-Monte Carlo method to this problem is often only marginally more efficient than the classical Monte Carlo method. Using the dimension reduction technique of [Imai, J., Tan, K.S., 2007. A general dimension reduction method for derivative pricing. J. Comput. Financ. 10 (2), 129–155] it is possible to significantly reduce the effective dimension of the problem. The paper shows why the proposed technique leads to a dramatic improvement in efficiency.     

Bayesian Variable Selection via Particle Stochastic Search

We focus on Bayesian variable selection in regression models. One challenge is to search the huge model space adequately, while identifying high posterior probability regions. In the past decades, the main focus has been on the use of Markov chain Monte Carlo (MCMC) algorithms for these purposes. In this article, we propose a new computational approach based on sequential Monte Carlo (SMC), which we refer to as particle stochastic search (PSS). We illustrate PSS through applications to linear regression and probit models.     

具有GARCH-skew-t误差项的时序的单位根检验

本文通过随机模拟,分析条件分布为偏t分布、具有自回归条件异方差误差项的时间序列的ADF单位根检验的临界值、检验的有效性和实际显著水平的扭曲分析。结果显示,随着波动持久性的增强,已不能直接使用Fu ller的临界值表。     

Continuum percolation with steps in the square or the disc

In 1961 Gilbert defined a model of continuum percolation in which points are placed in the plane according to a Poisson process of density 1, and two are joined if one lies within a disc of area A about the other. We prove some good bounds on the critical area A_c for percolation in this model. The proof is in two parts: First we give a rigorous reduction of the problem to a finite problem, and then we solve this problem using Monte‐Carlo methods. We prove that, with 99.99% confidence, the critical area lies between 4.508 and 4.515. For the corresponding problem with the disc replaced by the square we prove, again with 99.99% confidence, that the critical area lies between 4.392 and 4.398. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Monte Carlo EM加速算法

EM算法是近年来常用的求后验众数的估计的一种数据增广算法, 但由于求出其E步中积分的显示表达式有时很困难, 甚至不可能, 限制了其应用的广泛性. 而Monte Carlo EM算法很好地解决了这个问题, 将EM算法中E步的积分用Monte Carlo模拟来有效实现, 使其适用性大大增强. 但无论是EM算法, 还是Monte Carlo EM算法, 其收敛速度都是线性的, 被缺损信息的倒数所控制, 当缺损数据的比例很高时, 收敛速度就非常缓慢. 而Newton-Raphson算法在后验众数的附近具有二次收敛速率. 本文提出Monte Carlo EM加速算法, 将Monte Carlo EM算法与Newton-Raphson算法结合, 既使得EM算法中的E步用Monte Carlo模拟得以实现, 又证明了该算法在后验众数附近具有二次收敛速度. 从而使其保留了Monte Carlo EM算法的优点, 并改进了Monte Carlo EM算法的收敛速度. 本文通过数值例子, 将Monte Carlo EM加速算法的结果与EM算法、Monte Carlo EM算法的结果进行比较, 进一步说明了Monte Carlo EM加速算法的优良性.     

基于信用风险修正的多阶段银行资产组合优化模型

从资产组合管理角度出发,用信用风险修正的方法对企业信用等级阈值进行修正,同时考虑商业银行持续经营的特点,将修正后的信用风险引入到多阶段的模型当中去,建立一个基于信用风险修正的多阶段银行资产组合优化模型.针对该模型的特点,给出了把Monte Carlo模拟的动态算法和改进粒子群的多阶段算法相结合求解方法.数值试验表明所建...     

Unit Root Testing in Presence of a Double Threshold Process

In this paper we propose a double threshold process that generalizes the threshold autoregressive one widely known in the literature. It is characterized by a structure with two thresholds: the first regulates the switching between two autoregressive regimes; the second threshold regulates the switching between the two regimes of the stationary innovations. A testing procedure based on a Wald statistic has been given to evaluate the presence of unit roots in the process against stationarity. The asymptotic distribution of the statistic has been derived and the size and the power of the test have been evaluated through a Monte Carlo study where the proposed test is compared to two competing unit root testing procedures. The results clearly highlight the advantage obtained from the proposed test as the asymmetry of the generating process increases.     

Fracture in Ceramic-Matrix Composites Reinforced with Strongly Bonded Metal Particles

The resistance of a ceramic matrix composite to the cleavage cracking across a field of strongly bonded, uniformly distributed metal particles is studied. The crack trapping and bridging effects of the metal particles are analyzed by means of calculating the strain energy and the traction work. An explicit expression for the critical energy release rate as a function of particle volume fraction has been obtained. The fracture resistance is independent of elastic properties of the matrix and the sample geometry and is predominantly determined by the size/spacing ratio of the particles. It is shown that the theoretical curves agree with experimental data quite well. The methodology developed in this article can be used in studying the fracture resistances of composites with high filler contents and irregular filler geometries.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 303–318, May–June, 2005.     

Global Optimization Performance Measures for Generalized Hill Climbing Algorithms

Generalized hill climbing algorithms provide a framework for modeling several local search algorithms for hard discrete optimization problems. This paper introduces and analyzes generalized hill climbing algorithm performance measures that reflect how effectively an algorithm has performed to date in visiting a global optimum and how effectively an algorithm may pes]rform in the future in visiting such a solution. These measures are also used to obtain a necessary asymptotic convergence (in probability) condition to a global optimum, which is then used to show that a common formulation of threshold accepting does not converge. These measures assume particularly simple forms when applied to specific search strategies such as Monte Carlo search and threshold accepting.     

Minimal relative entropy for equivalent martingale measures by low-discrepancy sequence in Lévy process

In this paper, we focused on computing the minimal relative entropy between the original probability and all of the equivalent martin gale measure for the Lévy process. For this purpose, the quasiMonte Carlo method is used. The probability with minimal relative entropy has many suitable properties. This probability has the minimal Kullback-Leibler distance to the original probability. Also, by using the minimal relative entropy the exponential utility indifference price can be found. In this paper, the Monte Carlo and quasi-Monte Carlo methods have been applied. In the quasi-Monte Carlo method, two types of widely used lowdiscrepancy sequences, Halton sequence and Sobol sequence, are used. These methods have been used for exponential Lévy process such as variance gamma and CGMY process. In these two processes, the minimal relative entropy has been computed by Monte Carlo and quasi-Monte Carlo, and compared their results. The results show that quasi-Monte Carlo with Sobol sequence performs better in terms of fast convergence and less error. Finally, this method by fitting the variance gamma model and parameters estimation for the model has been implemented for financial data and the corresponding minimal relative entropy has been computed.     

层次分析法一致性指标的临界值研究

层次分析法中一致性检验的显著性水平(即判断矩阵偏离一致性的程度)问题在已有研究文献中尚未得到很好的解决。论文在现有一致性指标CI基础上,从随机过程的视角,采用蒙特卡罗模拟法构造一致性指标的随机样本,根据样本确定了显著性水平为0.05和0.01情形下对应的一致性指标的临界值,为评价和调整判断矩阵提供了理论标准。同时,本研究能够确定判断矩阵偏离一致性的程度,并给出决策制定的显著性水平。     

电力系统可靠性的蒙特卡洛方法

本文首先对中国科学技术大学管理科研楼电力系统可靠度评估建立了线性传感器模型。由于线性传感器可靠度评估是一个#P问题,没有多项式时间的算法。所以本文运用了蒙特卡罗方法,考虑到未加改进的蒙特卡洛方法对于解决本身可靠度很高的系统时的效率非常低,本文使用了广泛应用于网络可靠性的RVR(Recursive Variance Reduction)方法,给出了可靠度的测算结果。     

Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation.     

Parallel Speed-Up of Monte Carlo Methods for Global Optimization

We introduce the notion of expected hitting time to a goal as a measure of the convergence rate of a Monte Carlo optimization method. The techniques developed apply to simulated annealing, genetic algorithms, and other stochastic search schemes. The expected hitting time can itself be calculated from the more fundamental complementary hitting time distribution (CHTD) which completely characterizes a Monte Carlo method. The CHTD is asymptotically a geometric series, (1/s)/(1 − λ), characterized by two parameters, s, λ, related to the search process in a simple way. The main utility of the CHTD is in comparing Monte Carlo algorithms. In particular we show that independent, identical Monte Carlo algorithms run in parallel, IIP parallelism, and exhibit superlinear speedup. We give conditions under which this occurs and note that equally likely search is linearly sped up. Further we observe that a serial Monte Carlo search can have an infinite expected hitting time, but the same algorithm when parallelized can have a finite expected hitting time. One consequence of the observed superlinear speedup is an improved uniprocessor algorithm by the technique of in-code parallelism.