Simulation and the monte carlo method
01 Mar 1982-Bulletin of The London Mathematical Society (Oxford University Press (OUP))-Vol. 14, Iss: 2, pp 174-175
About: This article is published in Bulletin of The London Mathematical Society.The article was published on 1982-03-01. It has received 1196 citations till now. The article focuses on the topics: Dynamic Monte Carlo method & Hybrid Monte Carlo.
Citations
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TL;DR: In this article, the authors developed techniques for empirically analyzing demand and supply in differentiated products markets and then applied these techniques to analyze equilibrium in the U.S. automobile industry.
Abstract: This paper develops techniques for empirically analyzing demand and supply in differentiated products markets and then applies these techniques to analyze equilibrium in the U.S. automobile industry. Our primary goal is to present a framework which enables one to obtain estimates of demand and cost parameters for a class of oligopolistic differentiated products markets. These estimates can be obtained using only widely available product-level and aggregate consumer-level data, and they are consistent with a structural model of equilibrium in an oligopolistic industry. When we apply the tech- niques developed here to the U.S. automobile market, we obtain cost and demand parameters for (essentially) all models marketed over a twenty year period.
4,803 citations
Cites background from "Simulation and the monte carlo meth..."
...…often reduce the sampling variance of a simulation estimator of an integral by transforming both the integrand and the density we are drawing from in a way that reduces the variance of a simulation draw but leaves its expectation unchanged (see Rubinstein (1981), and the literature cited there)....
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TL;DR: In this article, the authors address Ronkko and Evermann's criticisms of the Partial Least Squares (PLS) approach to structural equation modeling and conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines.
Abstract: This article addresses Ronkko and Evermann’s criticisms of the partial least squares (PLS) approach to structural equation modeling. We contend that the alleged shortcomings of PLS are not due to problems with the technique, but instead to three problems with Ronkko and Evermann’s study: (a) the adherence to the common factor model, (b) a very limited simulation designs, and (c) overstretched generalizations of their findings. Whereas Ronkko and Evermann claim to be dispelling myths about PLS, they have in reality created new myths that we, in turn, debunk. By examining their claims, our article contributes to reestablishing a constructive discussion of the PLS method and its properties. We show that PLS does offer advantages for exploratory research and that it is a viable estimator for composite factor models. This can pose an interesting alternative if the common factor model does not hold. Therefore, we can conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines.
1,906 citations
TL;DR: This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO), where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases.
Abstract: This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields,singularity in some cases.
935 citations
Cites background or methods from "Simulation and the monte carlo meth..."
...The Monte Carlo simulation (MCS) (Rubinstein, 1981) provides a convenient approximation for both reliability analysis and inverse reliability analysis because it directly approximates the βG~g relationship....
[...]
...The minimum MCS sample size for finding the point (βa, ga) is usually suggested as L = 10 P G a( ( ) )x ≤ g = 10 F gG a( ) = 10 Φ( )−βa (16) where L increases exponentially in terms of βa and becomes very large if the reliability target is high, e.g., L = 7692 for ga = 3....
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...If the Monte Carlo simulation (MCS) is used for probability analysis, the computational efforts required to find point (βs, 0) in RIA and point (βt, g*) in PMA can be quantified by the minimum MCS sample size L suggested in Eq....
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...X ( ) )nG( ) xx ga x x xiL i iU≤ ≤ The Monte Carlo simulation (MCS) (Rubinstein, 1981) provides a convenient approximation for both reliability analysis and inverse reliability analysis because it directly approximates the βG~g relationship....
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...Thus, MCS becomes prohibitively expensive for many engineering applications....
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Book•
22 Dec 2015TL;DR: This book discusses Computational Statistics, a branch of Statistics, and its applications in medicine, education, and research.
Abstract: Prefaces Introduction What Is Computational Statistics? An Overview of the Book Probability Concepts Introduction Probability Conditional Probability and Independence Expectation Common Distributions Sampling Concepts Introduction Sampling Terminology and Concepts Sampling Distributions Parameter Estimation Empirical Distribution Function Generating Random Variables Introduction General Techniques for Generating Random Variables Generating Continuous Random Variables Generating Discrete Random Variables Exploratory Data Analysis Introduction Exploring Univariate Data Exploring Bivariate and Trivariate Data Exploring Multidimensional Data Finding Structure Introduction Projecting Data Principal Component Analysis Projection Pursuit EDA Independent Component Analysis Grand Tour Nonlinear Dimensionality Reduction Monte Carlo Methods for Inferential Statistics Introduction Classical Inferential Statistics Monte Carlo Methods for Inferential Statistics Bootstrap Methods Data Partitioning Introduction Cross-Validation Jackknife Better Bootstrap Confidence Intervals Jackknife-after-Bootstrap Probability Density Estimation Introduction Histograms Kernel Density Estimation Finite Mixtures Generating Random Variables Supervised Learning Introduction Bayes' Decision Theory Evaluating the Classifier Classification Trees Combining Classifiers Unsupervised Learning Introduction Measures of Distance Hierarchical Clustering K-Means Clustering Model-Based Clustering Assessing Cluster Results Parametric Models Introduction Spline Regression Models Logistic Regression Generalized Linear Models Nonparametric models Introduction Some Smoothing Methods Kernel Methods Smoothing Splines Nonparametric Regression-Other Details Regression Trees Additive Models Markov Chain Monte Carlo Methods Introduction Background Metropolis-Hastings Algorithms The Gibbs Sampler Convergence Monitoring Spatial Statistics Introduction Visualizing Spatial Point Processes Exploring First-Order and Second-Order Properties Modeling Spatial Point Processes Simulating Spatial Point Processes Appendix A: Introduction to Matlab What Is MATLAB? Getting Help in MATLAB File and Workspace Management Punctuation in MATLAB Arithmetic Operators Data Constructs in MATLAB Script Files and Functions Control Flow Simple Plotting Contact Information Appendix B: Projection Pursuit Indexes Indexes MATLAB Source Code Appendix C: Matlab Statistics Toolbox Appendix D: Computational Statistics Toolbox Appendix E: Exploratory Data Analysis Toolboxes Introduction EDA Toolbox EDA GUI Toolbox Appendix F: Data Sets Appendix G: NOTATION References INDEX MATLAB Code, Further Reading, and Exercises appear at the end of each chapter.
766 citations
Book•
13 Dec 1996
TL;DR: This book is devoted to providing a thorough and up-to-date survey of this field for researchers and students.
Abstract: Artificial intelligence and expert systems have seen a great deal of research in recent years, much of which has been devoted to methods for incorporating uncertainty into models. This book is devoted to providing a thorough and up-to-date survey of this field for researchers and students.
725 citations
Cites background from "Simulation and the monte carlo meth..."
...A classic reference to this field is Schank and Abelson (1977). Also, descriptions of language processing and language generation are found in Allen (1995) and McKeown (1985), respectively....
[...]
References
More filters
TL;DR: In this article, the authors developed techniques for empirically analyzing demand and supply in differentiated products markets and then applied these techniques to analyze equilibrium in the U.S. automobile industry.
Abstract: This paper develops techniques for empirically analyzing demand and supply in differentiated products markets and then applies these techniques to analyze equilibrium in the U.S. automobile industry. Our primary goal is to present a framework which enables one to obtain estimates of demand and cost parameters for a class of oligopolistic differentiated products markets. These estimates can be obtained using only widely available product-level and aggregate consumer-level data, and they are consistent with a structural model of equilibrium in an oligopolistic industry. When we apply the tech- niques developed here to the U.S. automobile market, we obtain cost and demand parameters for (essentially) all models marketed over a twenty year period.
4,803 citations
TL;DR: In this article, the authors address Ronkko and Evermann's criticisms of the Partial Least Squares (PLS) approach to structural equation modeling and conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines.
Abstract: This article addresses Ronkko and Evermann’s criticisms of the partial least squares (PLS) approach to structural equation modeling. We contend that the alleged shortcomings of PLS are not due to problems with the technique, but instead to three problems with Ronkko and Evermann’s study: (a) the adherence to the common factor model, (b) a very limited simulation designs, and (c) overstretched generalizations of their findings. Whereas Ronkko and Evermann claim to be dispelling myths about PLS, they have in reality created new myths that we, in turn, debunk. By examining their claims, our article contributes to reestablishing a constructive discussion of the PLS method and its properties. We show that PLS does offer advantages for exploratory research and that it is a viable estimator for composite factor models. This can pose an interesting alternative if the common factor model does not hold. Therefore, we can conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines.
1,906 citations
TL;DR: Statistical DownScaling Model (sdsm) facilitates the rapid development of multiple, low-cost, single-site scenarios of daily surface weather variables under current and future regional climate forcing.
Abstract: General Circulation Models (GCMs) suggest that rising concentrations of greenhouse gases will have significant implications for climate at global and regional scales. Less certain is the extent to which meteorological processes at individual sites will be affected. So-called ‘downscaling’ techniques are used to bridge the spatial and temporal resolution gaps between what climate modellers are currently able to provide and what impact assessors require. This paper describes a decision support tool for assessing local climate change impacts using a robust statistical downscaling technique. Statistical DownScaling Model (sdsm) facilitates the rapid development of multiple, low-cost, single-site scenarios of daily surface weather variables under current and future regional climate forcing. Additionally, the software performs ancillary tasks of predictor variable pre-screening, model calibration, basic diagnostic testing, statistical analyses and graphing of climate data. The application of sdsm is demonstrated with respect to the generation of daily temperature and precipitation scenarios for Toronto, Canada by 2040–2069. 2002 Elsevier Science Ltd. All rights reserved.
1,327 citations
TL;DR: This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO), where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases.
Abstract: This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields,singularity in some cases.
935 citations
Book•
22 Dec 2015TL;DR: This book discusses Computational Statistics, a branch of Statistics, and its applications in medicine, education, and research.
Abstract: Prefaces Introduction What Is Computational Statistics? An Overview of the Book Probability Concepts Introduction Probability Conditional Probability and Independence Expectation Common Distributions Sampling Concepts Introduction Sampling Terminology and Concepts Sampling Distributions Parameter Estimation Empirical Distribution Function Generating Random Variables Introduction General Techniques for Generating Random Variables Generating Continuous Random Variables Generating Discrete Random Variables Exploratory Data Analysis Introduction Exploring Univariate Data Exploring Bivariate and Trivariate Data Exploring Multidimensional Data Finding Structure Introduction Projecting Data Principal Component Analysis Projection Pursuit EDA Independent Component Analysis Grand Tour Nonlinear Dimensionality Reduction Monte Carlo Methods for Inferential Statistics Introduction Classical Inferential Statistics Monte Carlo Methods for Inferential Statistics Bootstrap Methods Data Partitioning Introduction Cross-Validation Jackknife Better Bootstrap Confidence Intervals Jackknife-after-Bootstrap Probability Density Estimation Introduction Histograms Kernel Density Estimation Finite Mixtures Generating Random Variables Supervised Learning Introduction Bayes' Decision Theory Evaluating the Classifier Classification Trees Combining Classifiers Unsupervised Learning Introduction Measures of Distance Hierarchical Clustering K-Means Clustering Model-Based Clustering Assessing Cluster Results Parametric Models Introduction Spline Regression Models Logistic Regression Generalized Linear Models Nonparametric models Introduction Some Smoothing Methods Kernel Methods Smoothing Splines Nonparametric Regression-Other Details Regression Trees Additive Models Markov Chain Monte Carlo Methods Introduction Background Metropolis-Hastings Algorithms The Gibbs Sampler Convergence Monitoring Spatial Statistics Introduction Visualizing Spatial Point Processes Exploring First-Order and Second-Order Properties Modeling Spatial Point Processes Simulating Spatial Point Processes Appendix A: Introduction to Matlab What Is MATLAB? Getting Help in MATLAB File and Workspace Management Punctuation in MATLAB Arithmetic Operators Data Constructs in MATLAB Script Files and Functions Control Flow Simple Plotting Contact Information Appendix B: Projection Pursuit Indexes Indexes MATLAB Source Code Appendix C: Matlab Statistics Toolbox Appendix D: Computational Statistics Toolbox Appendix E: Exploratory Data Analysis Toolboxes Introduction EDA Toolbox EDA GUI Toolbox Appendix F: Data Sets Appendix G: NOTATION References INDEX MATLAB Code, Further Reading, and Exercises appear at the end of each chapter.
766 citations