Download or read book Sequential Monte Carlo Parameter Estimation for Differential Equations written by Andrea Arnold and published by . This book was released on 2014 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: A central problem in numerous applications is estimating the unknown parameters of a system of ordinary differential equations (ODEs) from noisy measurements of a function of some of the states at discrete times. Formulating this dynamic inverse problem in a Bayesian statistical framework, state and parameter estimation can be performed using sequential Monte Carlo (SMC) methods, such as particle filters (PFs) and ensemble Kalman filters (EnKFs).Addressing the issue of particle retention in PF-SMC, we propose to solve ODE systems within a PF framework with higher order numerical integrators which can handle stiffness and to base the choice of the innovation variance on estimates of discretization errors. Using linear multistep method (LMM) numerical solvers in this context gives a handle on the stability and accuracy of propagation, and provides a natural and systematic way to rigorously estimate the innovation variance via well-known local error estimates.We explore computationally efficient implementations of LMM PF-SMC by considering parallelized and vectorized formulations. While PF algorithms are known to be amenable to parallelization due to the independent propagation of each particle, by formulating the problem in a vectorized fashion, it is possible to arrive at an implementation of the method which takes full advantage of multiple processors.We employ a variation of LMM PF-SMC in estimating unknown parameters of a tracer kinetics model from sequences of real positron emission tomography scan data. A combination of optimization and statistical inference is utilized: nonlinear least squares finds optimal starting values, which then act as hyperparameters in the Bayesian framework. The LMM PF-SMC algorithm is modified to allow variable time steps to accommodate the increase in time interval length between data measurements from beginning to end of the procedure, keeping the time step the same for each particle.We also apply the idea of linking innovation variance with numerical integration error estimates to EnKFs by employing a stochastic interpretation of the discretization error in numerical integrators, extending the technique to deterministic, large-scale nonlinear evolution models. The resulting algorithm, which introduces LMM time integrators into the EnKF framework, proves especially effective in predicting unmeasured system components.

Download or read book An Introduction to Sequential Monte Carlo written by Nicolas Chopin and published by Springer Nature. This book was released on 2020-10-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 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 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.

Download or read book Parameter Estimation Using Sequential Monte Carlo written by Mohd. Fariduddin Mukhtar and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parameter Estimation Using Sequential Monte Carlo written by Mohd. Fariduddin Mukhtar and published by . This book was released on 2012 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sequential Monte Carlo Methods for Parameter Estimation Dynamic State Estimation and Control in Power Systems written by Daniel Adrian Maldonado and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimating the Parameters of Stochastic Differential Equations by Monte Carlo Methods written by A. Stan Hurn and published by . This book was released on 1995 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sequential Monte Carlo Smoothing with Application to Parameter Estimation in Non linear State Space Models written by Jimmy Olsson and published by . This book was released on 2006 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Download or read book Stochastic Simulation and Monte Carlo Methods written by Carl Graham and published by Springer Science & Business Media. This book was released on 2013-07-16 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.

Download or read book Parameter Estimation for State Space Models Using Sequential Monte Carlo Methods and State Augmentation written by Scott Peter Wile and published by . This book was released on 2008 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Stability of Sequential Monte Carlo Methods for Parameter Estimation written by Bernd Kuhlenschmidt and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parameter Estimation for State Space Models Using Sequential Monte Carlo Algorithms written by Christopher Nemeth and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2009-06-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.

Download or read book Introduction to Monte Carlo Methods for Transport and Diffusion Equations written by Bernard Lapeyre and published by OUP Oxford. This book was released on 2003 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is used by for the resolution of partial differential equations, trasnport equations, the Boltzmann equation and the parabolic equations of diffusion.