Download or read book A Monte Carlo Approach to the Evaluation of Conditional Expectation Parameter Estimates for Nonlinear Dynamic Systems written by R. B. McGhee and published by . This book was released on 1967 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conditional Monte Carlo written by Michael C. Fu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditional Monte Carlo: Gradient Estimation and Optimization Applications deals with various gradient estimation techniques of perturbation analysis based on the use of conditional expectation. The primary setting is discrete-event stochastic simulation. This book presents applications to queueing and inventory, and to other diverse areas such as financial derivatives, pricing and statistical quality control. To researchers already in the area, this book offers a unified perspective and adequately summarizes the state of the art. To researchers new to the area, this book offers a more systematic and accessible means of understanding the techniques without having to scour through the immense literature and learn a new set of notation with each paper. To practitioners, this book provides a number of diverse application areas that makes the intuition accessible without having to fully commit to understanding all the theoretical niceties. In sum, the objectives of this monograph are two-fold: to bring together many of the interesting developments in perturbation analysis based on conditioning under a more unified framework, and to illustrate the diversity of applications to which these techniques can be applied. Conditional Monte Carlo: Gradient Estimation and Optimization Applications is suitable as a secondary text for graduate level courses on stochastic simulations, and as a reference for researchers and practitioners in industry.
Download or read book Parametric Estimates by the Monte Carlo Method written by Gennadij Alekseevič Michajlov and published by VSP. This book was released on 1999 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the further development of parametric weight Monte Carlo estimates for solving linear and nonlinear integral equations, radiation transfer equations, and boundary value problems, including problems with random parameters. The use of these estimates leads to the construction of new, effective Monte Carlo methods for calculating parametric multiple derivatives of solutions and for the main eigenvalues. The book opens with an introduction on the theory of weight Monte Carlo methods. The following chapters contain new material on solving boundary value problems with complex parameters, mixed problems to parabolic equations, boundary value problems of the second and third kind, and some improved techniques related to vector and nonlinear Helmholtz equations. Special attention is given to the foundation and optimization of the global 'walk on grid' method for solving the Helmholtz difference equation. Additionally, new Monte Carlo methods for solving stochastic radiation transfer problems are presented, including the estimation of probabilistic moments of corresponding critical parameters.
Download or read book Bayesian Statistics 2 written by J. M. Bernardo and published by . This book was released on 1985 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Monte Carlo Methods for Data Assimilation in Strongly Nonlinear Dynamics written by Zhiyu Wang and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data assimilation is the process of estimating the state of dynamic systems (linear or nonlinear, Gaussian or non-Gaussian) as accurately as possible from noisy observational data. Although the Three Dimensional Variational (3D-VAR) methods, Four Dimensional Variational (4D-VAR) methods and Ensemble Kalman filter (EnKF) methods are widely used and effective for linear and Gaussian dynamics, new methods of data assimilation are required for the general situation, that is, nonlinear non-Gaussian dynamics. General Bayesian recursive estimation theory is reviewed in this thesis. The Bayesian estimation approach provides a rather general and powerful framework for handling nonlinear, non-Gaussian, as well as linear, Gaussian estimation problems. Despite a general solution to the nonlinear estimation problem, there is no closed-form solution in the general case. Therefore, approximate techniques have to be employed. In this thesis, the sequential Monte Carlo (SMC) methods, commonly referred to as the particle filter, is presented to tackle non-linear, non-Gaussian estimation problems. In this thesis, we use the SMC methods only for the nonlinear state estimation problem, however, it can also be used for the nonlinear parameter estimation problem. In order to demonstrate the new methods in the general nonlinear non-Gaussian case, we compare Sequential Monte Carlo (SMC) methods with the Ensemble Kalman Filter (EnKF) by performing data assimilation in nonlinear and non-Gaussian dynamic systems. The models used in this study are referred to as state-space models. The Lorenz 1963 and 1966 models serve as test beds for examining the properties of these assimilation methods when used in highly nonlinear dynamics. The application of Sequential Monte Carlo methods to different fixed parameters in dynamic models is considered. Four different scenarios in the Lorenz 1063 [sic] model and three different scenarios in the Lorenz 1996 model are designed in this study for both the SMC methods and EnKF method with different filter size from 50 to 1000. The comparison results show that the SMC methods have theoretical advantages and also work well with highly nonlinear Lorenz models for state estimation in practice. Although Ensemble Kalman Filter (EnKF) computes only the mean and the variance of the state, which is based on linear state-space models with Gaussian noise, the SMC methods do not outperform EnKF in practical applications as we expected in theoretical insights. The main drawback of Sequential Monte Carlo (SMC) methods is that it requires much computational power, which is the obstacle to extend SMC methods to high dimensional atmospheric and oceanic models. We try to interpret the reason why the SMC data assimilation result is similar to the EnKF data assimilation result in these experiments and discuss the potential future application for high dimensional realistic atmospheric and oceanic models in this thesis.
Download or read book Current Technical Papers written by and published by . This book was released on 1968 with total page 978 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Monte Carlo Methods for Nonlinear Discrete Time Filtering written by Marcelo G. S. Bruno and published by Morgan & Claypool Publishers. This book was released on 2013-01-01 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary
Download or read book Identification and Process Parameter Estimation written by and published by . This book was released on 1970 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Actuarial Research Clearing House written by and published by . This book was released on 1985 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Monte Carlo Analysis of the Conditional Forecasting Performance of a Nondynamic Econometric Model written by William L. Fitzsimmons and published by . This book was released on 1989 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Methods and Stochastic Processes written by Emmanuel Gobet and published by CRC Press. This book was released on 2016-09-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.
Download or read book Evolution and Optimum Seeking written by Hans-Paul Schwefel and published by Wiley-Interscience. This book was released on 1995-01-23 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical optimization methods and algorithms applied to computer calculations. The methods consist of the adaptation of simple evolutionary rules to a computer procedure which is to search for optimal parameters within a simulation model of a technical device. Accompanied by a diskette containing the algorithms presented in the book.
Download or read book New Monte Carlo Methods With Estimating Derivatives written by Gennadij A. Michajlov and published by VSP. This book was released on 1995-01-01 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is possible to use weighted Monte Carlo methods for solving many problems of mathematical physics (boundary value problems for elliptic equations, the Boltzmann equation, radiation transfer and diffusion equations). Weight estimates make it possible to evaluate special functionals, for example, derivatives with respect to parameters of a problem. In this book new weak conditions are presented under which the corresponding vector Monte Carlo estimates are unbiased and their variances are finite. The author has also constructed new Monte Carlo methods for solving the Helmholz equation with a nonconstant parameter, including the stationary Schrodinger equation. New results for linear and nonlinear problems are also presented. Some methods of random function simulation are considered in the special appendix. A new method of substantiating and optimizing the reccurent Monte Carlo estimates without using the Neumann series is presented in the introduction.
Download or read book Sequential Monte Carlo Methods in Practice written by Arnaud Doucet and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.
Download or read book Parameter Identification and State Estimation for Linear Systems written by Michael Allan Budin and published by . This book was released on 1969 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1995 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Monte Carlo Methods written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
