An Introduction To Sequential Monte Carlo
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An Introduction To Sequential Monte Carlo
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Author : Nicolas Chopin
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
An Introduction To Sequential Monte Carlo written by Nicolas Chopin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.
This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book. Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed. The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a “Python corner,” which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.
Sequential Monte Carlo Methods In Practice
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Author : Arnaud Doucet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Sequential Monte Carlo Methods In Practice written by Arnaud Doucet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering
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Author : Marcelo G.
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering written by Marcelo G. and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.
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
Elements Of Sequential Monte Carlo
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Author : Christian A. Naesseth
language : en
Publisher:
Release Date : 2019-11-12
Elements Of Sequential Monte Carlo written by Christian A. Naesseth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-12 with Computers categories.
Written in a tutorial style, this monograph introduces the basics of Sequential Monte Carlo, discusses practical issues, and reviews theoretical results before guiding the reader through a series of advanced topics to give a complete overview of the topic and its application to machine learning problems.
Fast Sequential Monte Carlo Methods For Counting And Optimization
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Author : Reuven Y. Rubinstein
language : en
Publisher: John Wiley & Sons
Release Date : 2013-11-13
Fast Sequential Monte Carlo Methods For Counting And Optimization written by Reuven Y. Rubinstein and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-13 with Mathematics categories.
A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems. Written by authorities in the field, the book places emphasis on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration. Focusing on the concepts and application of Monte Carlo techniques, Fast Sequential Monte Carlo Methods for Counting and Optimization includes: Detailed algorithms needed to practice solving real-world problems Numerous examples with Monte Carlo method produced solutions within the 1-2% limit of relative error A new generic sequential importance sampling algorithm alongside extensive numerical results An appendix focused on review material to provide additional background information Fast Sequential Monte Carlo Methods for Counting and Optimization is an excellent resource for engineers, computer scientists, mathematicians, statisticians, and readers interested in efficient simulation techniques. The book is also useful for upper-undergraduate and graduate-level courses on Monte Carlo methods.
Elements Of Sequential Monte Carlo
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Author : CHRISTIAN A. NAESSETH;FREDRIK LINDSTEN;THOMAS B. S.
language : en
Publisher:
Release Date : 2019
Elements Of Sequential Monte Carlo written by CHRISTIAN A. NAESSETH;FREDRIK LINDSTEN;THOMAS B. S. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Written in a tutorial style, this monograph introduces the basics of Sequential Monte Carlo, discusses practical issues, and reviews theoretical results before guiding the reader through a series of advanced topics to give a complete overview of the topic and its application to machine learning problems.
Monte Carlo Methods
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Author : Adrian Barbu
language : en
Publisher: Springer Nature
Release Date : 2020-02-24
Monte Carlo Methods written by Adrian Barbu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-24 with Mathematics categories.
This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering
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Author : Marcelo G. S. Bruno
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2013
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering written by Marcelo G. S. Bruno and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
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.
Simulation And The Monte Carlo Method
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Author : Reuven Y. Rubinstein
language : en
Publisher: John Wiley & Sons
Release Date : 2016-11-07
Simulation And The Monte Carlo Method written by Reuven Y. Rubinstein and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-07 with Mathematics categories.
This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples. The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on: • Random number generation, including multiple-recursive generators and the Mersenne Twister • Simulation of Gaussian processes, Brownian motion, and diffusion processes • Multilevel Monte Carlo method • New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters • Over 100 algorithms in modern pseudo code with flow control • Over 25 new exercises Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting. Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.
Introducing Monte Carlo Methods With R
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Author : Christian Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2010
Introducing Monte Carlo Methods With R written by Christian Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
This book 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.