Download or read book Adaptive Control Variates in Monte Carlo Simulation written by Sujin Kim and published by . This book was released on 2006 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Constructive and Generic Control Variates for Monte Carlo Estimation written by Tarik Borogovac and published by . This book was released on 2009 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Estimation of quantities that can be represented as expectations of appropriately defined random variables is an important problem in diverse areas of science and engineering. Monte Carlo (MC) sampling/simulation is a very general approach for estimation, and is the method of choice in many application areas. To increase the computational efficiency of MC simulation a number of Variance Reduction Techniques (VRT), which aim to reduce the variance of the MC estimator, have been devised. The design of effective VRT's has so far relied on the existence of specific problem features, and the acuity of the user to discover and properly exploit such features. One of the most effective VRT's is the method of Control Variates (CV). This method relies on a number of auxiliary random variables, called controls, that carry information about the estimation variable and "explain" part of its variance. If the means of the controls are known, or high quality estimates of them are available, the CV technique prescribes a generic procedure for transferring the relevant information to the estimation variable, leading to a controlled estimator with smaller variance. The main difficulty with the CV technique is in discovering controls that are informative about the estimation variable. This thesis presents a generic approach to the selection controls that is applicable to a broad class of problems where the estimation variable depends on a model parameter. It is shown that, under conditions, information at a set of parameters can be used to define effective controls for estimation at neighboring parameters. A connection between sample-wise function approximation methods and the CV method is established. Motivated by this connection, controls for the estimation variable and for its sensitivity with respect to the parameter are proposed. Their effectiveness is demonstrated on simulations from the fields of finance, materials science and photon transport. The requirement of tractability of controls is replaced by generic computational procedures through which the necessary information about the controls is procured. Two alternative algorithms that perform this function are given, and the CV estimators that result are analyzed.
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2008 written by Pierre L' Ecuyer and published by Springer Science & Business Media. This book was released on 2010-01-14 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Eighth International Conference on Monte Carlo (MC)and Quasi-Monte Carlo (QMC) Methods in Scientific Computing, held in Montreal (Canada) in July 2008. It covers the latest theoretical developments as well as important applications of these methods in different areas. It contains two tutorials, eight invited articles, and 32 carefully selected articles based on the 135 contributed presentations made at the conference. This conference is a major event in Monte Carlo methods and is the premiere event for quasi-Monte Carlo and its combination with Monte Carlo. This series of proceedings volumes is the primary outlet for quasi-Monte Carlo research.
Download or read book Monte Carlo Methods written by J. Hammersley and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness.
Download or read book Regression based Monte Carlo Methods with Optimal Control Variates written by Stefan Häfner and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by Wiley-Interscience. This book was released on 1981-05-14 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.
Download or read book Control Variates for Monte Carlo Analysis of Nonlinear Statitical sic Models written by James J. Swain and published by . This book was released on 1989 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Control Variate Approach for Multi user Estimation Via Monte Carlo Simulation written by Na Sun and published by . This book was released on 2013 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Monte Carlo (MC) simulation forms a very flexible and widely used computational method employed in many areas of science and engineering. The focus of this research is on the variance reduction technique of Control Variates (CV) which is a statistical approach used to improve the efficiency of MC simulation. We consider parametric estimation problems encountered in analysing stochastic systems where the stochastic system performance or its sensitivity depends on some model or decision parameter. Furthermore, we assume that the estimation is performed by one or more users at one or several parameter values. A store and reuse setting is introduced where at a set-up stage sonic information is gathered computationally and stored. The stored information is then used at the estimation phase by users to help with their estimation problems.Three problems in this setting are addressed. (i) An analysis of the user's choices at the estimation phase is provided. The information generated at the set-up phase is stored in the form of information about a set of random variables that can be used as control variates. Users need to decide whether, and if so how, to use the stored information. A so-called cost-adjusted mean squared error is used as a measure cost of the available estimators and user's decision is formulated as a constrained minimization problem. (ii) A recent approach to defining generic control variates in parametric estimation problems is generalized in two distinct directions: the first involves considering an alternative parametrization of the original problem through a change of probability measure. This parametrization is particularly relevant to sensitivity estimation problems with respect to model and decision parameters. In the second, for problems where the quantities of interest are defined on sample paths of stochastic processes that model the underlying stochastic dynamics, systematic control variate selection based on approximate dynamics is proposed. (iii) When common random inputs are used parametric estimation variables become statistically dependent. This dependence is explicitly modelled as a random field and conditions are derived to imply the effectiveness of estimation variables as control variates. Comparisons with the metamodeling approach of Kriging and recently proposed Stochastic Kriging that use similar inputs data to predict the mean of the estimation variable are provided.
Download or read book Adaptive Stochastic Methods written by Dmitry G. Arseniev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-01-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics. Contents Part I: Evaluation of Integrals Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals Sequential Monte Carlo Method and Adaptive Integration Methods of Adaptive Integration Based on Piecewise Approximation Methods of Adaptive Integration Based on Global Approximation Numerical Experiments Adaptive Importance Sampling Method Based on Piecewise Constant Approximation Part II: Solution of Integral Equations Semi-Statistical Method of Solving Integral Equations Numerically Problem of Vibration Conductivity Problem on Ideal-Fluid Flow Around an Airfoil First Basic Problem of Elasticity Theory Second Basic Problem of Elasticity Theory Projectional and Statistical Method of Solving Integral Equations Numerically
Download or read book Monte Carlo and Quasi Monte Carlo Methods written by Bruno Tuffin and published by Springer Nature. This book was released on 2020-05-01 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Rennes, France, and organized by Inria, in July 2018. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.
Download or read book Reliable Quasi Monte Carlo with Control Variates written by Da Li and published by . This book was released on 2016 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The use of control variates in Monte Carlo estimation of power curves written by P. Rothery and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introducing Monte Carlo Methods with R written by Christian Robert and published by Springer Science & Business Media. This book was released on 2009-11-24 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational techniques based on simulation have now become an essential part of the statistician's toolbox. It is thus crucial to provide statisticians with a practical understanding of those methods, and there is no better way to develop intuition and skills for simulation than to use simulation to solve statistical problems. Introducing Monte Carlo Methods with R covers the main tools used in statistical simulation from a programmer's point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison. While this book constitutes a comprehensive treatment of simulation methods, the theoretical justification of those methods has been considerably reduced, compared with Robert and Casella (2004). Similarly, the more exploratory and less stable solutions are not covered here. This book does not require a preliminary exposure to the R programming language or to Monte Carlo methods, nor an advanced mathematical background. While many examples are set within a Bayesian framework, advanced expertise in Bayesian statistics is not required. The book covers basic random generation algorithms, Monte Carlo techniques for integration and optimization, convergence diagnoses, Markov chain Monte Carlo methods, including Metropolis {Hastings and Gibbs algorithms, and adaptive algorithms. All chapters include exercises and all R programs are available as an R package called mcsm. The book appeals to anyone with a practical interest in simulation methods but no previous exposure. It is meant to be useful for students and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The programming parts are introduced progressively to be accessible to any reader.
Download or read book Sequential Monte Carlo Methods for Physically Based Rendering written by Shao Hua Fan and published by . This book was released on 2006 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Simulation and Finance written by Don L. McLeish and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.
Download or read book Monte Carlo methods written by John Michael Hammersley and published by . This book was released on 1964 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Optimization Simulation and Sensitivity of Queueing Networks written by Reuven Y. Rubinstein and published by . This book was released on 1986-09-02 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theoretical treatment of Monte Carlo optimization--simulation using perturbation analysis, adaptive methods, and variance reduction techniques. Emphasizes concepts rather than mathematical completeness. Shows how to use simulation and Monte Carlo methods efficiently for estimating performance measures, sensitivities and optimization of stochastic systems.
