An alternative teaching method of conditional probabilities and Bayes' rule: an application of the truth table

This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities—especially the ones that involve Bayes' rule—with the help of such traditional approaches as formula use or conversion to natural frequencies. The truth table approach is an alternative method for explaining the concept and calculation procedure of conditional probability and Bayes' rule.     

Simulation of scattering in dense medium by Monte Carlo method

We present a Monte Carlo (MC) method to simulate the scattering for medium within randomly distributed particles,discuss the convergence of this method by varying the size parameter ka, volume parameter ηand calculation parameter Ni, then compare this method with the classical iteration method with the same parameters. The calculation results showed that this method has good convergence and accords with the iteration method while consuming less CPU time. At the end of this paper, this method is used to discuss the visual light scatter in the c-Si/α-Si films.     

Dynamic Monte Carlo simulation of linear SAW polymer chain near a flat surface

INTRODUCTION The conformational property of polymerchains subject to a geometrical constraint is one of themost interesting topics in polymer science (Milner,1991; Malfreyt and Tildesley, 2000; Vacatello,2001). The geometrical constraint can be a solidsurface, a liquid/liquid interface, a vacuum/liquidinterface, etc. So the topic has many applications intechnology such as adsorption onto interface, sta-bilization of colloids and partition equilibrium ingel permeation chromatography…     

Dynamic Monte Carlo simulation of linear SAW polymer chain near a flat surface

Investigation of the conformational properties of a SAW polymer chain near an impenetrable, non-interacting flat surface showed that the chain at first contracted and orientated itself to slightly parallel when it pulled close to the surface and at last elongated and reoriented itself to slightly perpendicular to the surface at very small distance from the surface. Simulation showed that most of the disappeared configurations were of large size at moderate distance from the surface while they were of small size at very small distance from the surface; and that the mean-square end-to-end distance was much more prone to be influenced by the surface than the mean-square radius of gyration . The orientational correlation between the direction of the longest principal axis of the moment of inertia and end-to-end vector was also discussed.     

Dynamic Monte Carlo study on the probability distribution functions of tail-like polymer chain

INTRODUCTION Polymer chains with one end attached to a sur- face by means of physical or chemical interaction have become one of the important polymer science subject, which are useful for many applications, such as polymer compatibilizers, copolymer microphases, colloid stabilization, polymeric surfactants (Milner, 1991). Grafting polymers can improve the power efficiency of electrorheological fluids, enhance pho- toluminescence of nano materials, and increase dis- persion stability. On …     

用Monte Carlo方法模拟基模Gauss光束

根据基模高斯光场，运用Monte Carlo随机模拟方法，实现了基模高斯光场的模拟，直观地说明了基模高斯光束的横模．     

带电粒子漂移运动的Monte Carlo模拟

讨论了带电粒子在外电场以及无外电场作用下的漂移运动的物理模型,并且讨论了电流导致导体升温情况下带电粒子的运动,使用Monte Carlo方法对其进行了动画模拟,形象地表现出带电粒子在各种情况下的运动状态．     

基于Monte Carlo模拟的宇宙线簇射发展研究

采用CORSIKA中的QGSJET强相互作用模型产生Monte Carlo的EAS事例样本,让所有Monte Carlo事例通过探测器阵列,形成Monte Carlo的观测事例样本。结果证实:通过研究宇宙线高能族事例发展,可以得到较理想的朝前区强子相互作用信息,从而能够有效的对目前正在使用的各种唯象模型的朝前区强子作用性质从TeV能区进行检验。     

理想气体扩散的Monte Carlo模拟

用Monte Carlo方法模拟了理想气体系统通过一小孔的扩散。模拟直观展现了气体分子通过小孔的扩散过程。模拟结果表明,一旦经过扩散达到平衡,系统将不会再回到最初的分布,这说明扩散过程是一个不可逆过程;在扩散过程中,系统的混乱程度不断增大。气体扩散快慢与初始分子数以及小孔的尺寸有关。初始分子数越多小尺寸越大,扩散过程进行的就越快。模拟结果与菲克定律一致。     

Random vibration analysis of switching apparatus based on Monte Carlo method

The performance in vibration environment of switching apparatus containing mechanical contact is an important element when judging the apparatus’s reliability. A piecewise linear two-degrees-of-freedom mathematical model considering contact loss was built in this work, and the vibration performance of the model under random external Gaussian white noise excitation was investigated by using Monte Carlo simulation in Matlab/Simulink. Simulation showed that the spectral content and statistical characters of the contact force coincided strongly with reality. The random vibration character of the contact system was solved using time (numerical) domain simulation in this paper. Conclusions reached here are of great importance for reliability design of switching apparatus.     

晶粒生长过程的蒙特卡罗模拟方法

计算机模拟晶粒生长所用的模型及模拟方法大体可分3种:蒙特卡罗(Monte Carlo)方法或改进的蒙特卡罗方法(简称MC法)、使用连续扩散界面场模型以及将细胞状的晶粒结构看作Laguere棋盘形布局来处理的Laguerre模型.特别是应用于模拟焊接热影响区(HAZ)晶粒长大的二维和三维过程取得了较好结果,但在生长模型的边界处理等方面有待继续完善,特别是晶粒生长与晶化温度、时间、气氛等参数密切相关,这种复杂工艺条件下的晶粒生长过程的模拟,是当前该领域正待解决的难题.     

蒙特卡罗方法在数学建模中的应用

蒙特卡罗方法是一个以概率模型为基础,利用计算机通过多次反复模拟实验完成问题求解的一种数值计算方法。它特别适用于用传统的解析法难以解决甚至是无法解决的问题。文章主要介绍蒙特卡罗方法及基本原理,并通过实例说明蒙特卡罗方法在数学建模中的应用。     

蒙特卡罗法预测含油气区石油资源量

石油勘探阶段,较准确地估算勘探地区的石油资源量是十分重要的。根据在勘探前所采集到的有限资料,并考虑到蒙特卡罗模拟在分析和求解复杂系统或样本数据少的情况下,更是一种不可缺少的分析技术。本文在随机变量的概率分布,计算局部含油地质单元的石油资源量,计算全局含油地质的石油资源量方面进行了较深入的研究,并通过利用各种数学理论和概率统计方面的知识和数学模型解决问题,按照模型的步骤采用Matlab7．1实现。     

Monte Carlo模拟在聚合反应速率常数估算中的运用

1 Introduction It is i mportant to study polymerization mechanisminpolymerization engineering. Obtaining kinetic data isthe key step for establishing polymerization mechanismand understanding elementary reactions . The kineticdata contains two groups of data ,i.e.,the rate andreaction order .The rate ,especially the rate constant ,is i mportant and to be esti mated assuming that the or-der of the reactionis known.Furthermore ,esti mationof rate constants for polymerization is an active anddif…     

超薄膜Si外延生长过程的动力学蒙特卡罗模拟

建立超薄膜Si外延生长的晶格一动力学蒙特卡罗模型,并应用该模型模拟了Si原子在Si（111）基底上外延生长的过程．系统研究了沉积时间、基片温度对于薄膜初始生长形貌的影响,如影响粒子的扩散与凝聚、岛的生长等微观过程．     

Examining and Controlling for Wording Effect in a Self-Report Measure: A Monte Carlo Simulation Study

Wording effect refers to the systematic method variance caused by positive and negative item wordings on a self-report measure. This Monte Carlo simulation study investigated the impact of ignoring wording effect on the reliability and validity estimates of a self-report measure. Four factors were considered in the simulation design: (a) the number of positively and negatively worded items, (b) the loadings on the trait and the wording effect factors, (c) sample size, and (d) the magnitude of population validity coefficient. The findings suggest that the unidimensional model that ignores the negative wording effect would underestimate the composite reliability and criterion-related validity, but overestimate the homogeneity coefficient. The magnitude of relative bias of the composite reliability was generally small and acceptable, whereas the relative bias for the homogeneity coefficient and criterion-related validity coefficient was negatively correlated with the strength of the general trait factor.     

拟蒙特卡罗积分与蒙特卡罗积分

分别介绍了蒙特卡罗方法和拟蒙特卡罗方法的基本思想,从算法本身、误差估计以及收敛率等角度分析了蒙特卡罗方法和拟蒙特卡罗方法的关系,并着重分析其在高维积分中的应用,从而说明拟蒙特卡罗方法的优越性。     

Modeling Unobserved Heterogeneity Using Latent Profile Analysis: A Monte Carlo Simulation

Latent profile analysis (LPA) has become a popular statistical method for modeling unobserved population heterogeneity in cross-sectionally sampled data, but very few empirical studies have examined the question of how well enumeration indexes accurately identify the correct number of latent profiles present. This Monte Carlo simulation study examined the ability of several classes of enumeration indexes to correctly identify the number of latent population profiles present under 3 different research design conditions: sample size, the number of observed variables used for LPA, and the separation distance among the latent profiles measured in Mahalanobis D units. Results showed that, for the homogeneous population (i.e., the population has k = 1 latent profile) conditions, many of the enumeration indexes used in LPA were able to correctly identify the single latent profile if variances and covariances were freely estimated. However, for a heterogeneous population (i.e., the population has k = 3 distinct latent profiles), the correct identification rate for the enumeration indexes in the k = 3 latent profile conditions was typically very low. These results are compared with the previous cross-sectional mixture modeling studies, and the limitations of this study, as well as future cross-sectional mixture modeling and enumeration index research possibilities, are discussed.     

模型设定偏误的蒙特卡洛模拟

设定偏误包括模型中遗漏变量和包含多余变量,会导致一些较严重的后果。在教学过程中,如果仅仅采用数学推导推演这些后果,由于公式复杂,学生接受较为困难;如果利用蒙特卡洛试验辅助教学,接受则会较为轻松。本研究利用GAUSS软件模拟模型设定偏误的后果。