Download or read book Particle Efficient Importance Sampling written by Marcel Scharth and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The efficient importance sampling (EIS) method is a general principle for the numerical evaluation of high-dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers. Despite a number of successful applications in high dimensions, it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases. We solve this problem by recognising that the EIS framework has an offline sequential Monte Carlo interpretation. The particle EIS method is based on non-standard resampling weights that take into account the look-ahead construction of the importance sampler. We apply the method for a range of univariate and bivariate stochastic volatility specifications. We also develop a new application of the EIS approach to state space models with Student's t state innovations. Our results show that the particle EIS method strongly outperforms both the standard EIS method and particle filters for likelihood evaluation in high dimensions. Moreover, the ratio between the variances of the particle EIS and particle filter methods remains stable as the time series dimension increases. We illustrate the efficiency of the method for Bayesian inference using the particle marginal Metropolis-Hastings and importance sampling squared algorithms.
Download or read book The Gibbs Sampler with Particle Efficient Importance Sampling for State Space Models written by Oliver Grothe and published by . This book was released on 2017 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider Particle Gibbs (PG) as a tool for Bayesian analysis of non-linear non-Gaussian state-space models. PG is a Monte Carlo (MC) approximation of the standard Gibbs procedure which uses sequential MC (SMC) importance sampling inside the Gibbs procedure to update the latent and potentially high-dimensional state trajectories. We propose to combine PG with a generic and easily implementable SMC approach known as Particle Efficient Importance Sampling (PEIS). By using SMC importance sampling densities which are approximately fully globally adapted to the targeted density of the states, PEIS can substantially improve the mixing and the efficiency of the PG draws from the posterior of the states and the parameters relative to existing PG implementations.The efficiency gains achieved by PEIS are illustrated in PG applications to a univariate stochastic volatility model for asset returns, a Gaussian nonlinear local-level model for interest rates, and a multivariate stochastic volatility model for the realized covariance matrix of asset returns.
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 Importance Sampling Methods with Multiple Sampling Distributions written by Wentao Li and published by . This book was released on 2013 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complexity of integrands in modern scientific, industrial and financial problems increases rapidly with the development of data collection technologies. Monte Carlo method is widely used for complicated integration. In Monte Carlo integration, it is a natural and flexible method to consider multiple simulation mechanisms instead of one to address different aspects of the integrand. New methods are needed to combine the multiple mechanisms efficiently. Monte Carlo integration methods are reviewed, with focus on importance sampling methods (IS) and sequential Monte Carlo methods (SMC). The former is commonly used for low-dimension problems. The latter is a variation of IS, which has been developed to be a new branch itself in the recent two decades, and promising for high- dimension problems with sequential nature. For IS, techniques for combining multiple proposal distributions have been well developed, including Owen and Zhou (2000) and Tan (2004). Important implementation issues are needed to be resolved, including the allocation of sample budgets and the selection of proposals. A two-stage procedure is proposed to optimize the sample allocation, and although little theoretical investigation has been done for such a two-stage procedure in literatures, its optimality among current approaches is theoretically justified. The choice of the first stage sample size is also discussed through investigating the high order performance of estimators. About the construction of proposals, suggestions are given to approximate the perfect case. For SMC, only the plain vanilla combination of multiple proposals has been used in literatures. A novel SMC filtering scheme is proposed to combine the multiple proposals through the control variates approach in Tan (2004). Control variates are used in both resampling and estimation. The new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates. The guidance for selecting multiple proposals and control variates is also given. Numerical studies of the AR(1) model observed with noise and the stochastic volatility model with AR(1) dynamics show that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter.
Download or read book Simulation based Econometric Methods written by Christian Gouriéroux and published by OUP Oxford. This book was released on 1997-01-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new generation of statistical econometrics. After linear models leading to analytical expressions for estimators, and non-linear models using numerical optimization algorithms, the availability of high- speed computing has enabled econometricians to consider econometric models without simple analytical expressions. The previous difficulties presented by the presence of integrals of large dimensions in the probability density functions or in the moments can be circumvented by a simulation-based approach. After a brief survey of classical parametric and semi-parametric non-linear estimation methods and a description of problems in which criterion functions contain integrals, the authors present a general form of the model where it is possible to simulate the observations. They then move to calibration problems and the simulated analogue of the method of moments, before considering simulated versions of maximum likelihood, pseudo-maximum likelihood, or non-linear least squares. The general principle of indirect inference is presented and is then applied to limited dependent variable models and to financial series.
Download or read book Particle Filtering and Parameter Learning written by Michael S. Johannes and published by . This book was released on 2011 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we provide an exact particle filtering and parameter learning algorithm. Our approach exactly samples from a particle approximation to the joint posterior distribution of both parameters and latent states, thus avoiding the use of and the degeneracies inherent to sequential importance sampling. Exact particle filtering algorithms for pure state filtering are also provided. We illustrate the efficiency of our approach by sequentially learning parameters and filtering states in two models. First, we analyze a robust linear state space model with t-distributed errors in both the observation and state equation. Second, we analyze a log-stochastic volatility model. Using both simulated and actual stock index return data, we find that algorithm efficiently learns all of the parameters and states in both models.
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 On Large Deviations and Design of Efficient Importance Sampling Algorithms written by and published by . This book was released on 2014 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin written by and published by . This book was released on 1910 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exploring Monte Carlo Methods written by William L. Dunn and published by Elsevier. This book was released on 2022-06-07 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Monte Carlo Methods, Second Edition provides a valuable introduction to the numerical methods that have come to be known as "Monte Carlo." This unique and trusted resource for course use, as well as researcher reference, offers accessible coverage, clear explanations and helpful examples throughout. Building from the basics, the text also includes applications in a variety of fields, such as physics, nuclear engineering, finance and investment, medical modeling and prediction, archaeology, geology and transportation planning. - Provides a comprehensive yet concise treatment of Monte Carlo methods - Uses the famous "Buffon's needle problem" as a unifying theme to illustrate the many aspects of Monte Carlo methods - Includes numerous exercises and useful appendices on: Certain mathematical functions, Bose Einstein functions, Fermi Dirac functions and Watson functions
Download or read book On the Use of Importance Sampling in Particle Transport Problems written by Bo Eriksson and published by . This book was released on 1965 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient High dimensional Importance Sampling in Mixture Frameworks written by Tore Selland Kleppe and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin written by United States. Bureau of Mines and published by . This book was released on 1936 with total page 1226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Independent Random Sampling Methods written by Luca Martino and published by Springer. This book was released on 2018-03-31 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general-purpose approaches, which can be used to generate samples from arbitrary probability distributions, and tailored techniques, designed to efficiently address common real-world practical problems, are introduced and discussed in detail. In turn, the monograph presents fundamental results and methodologies in the field, elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples, which are discussed in detail in the text and supplemented with ready-to-run computer code. The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field, address the latest methods, and emphasize the links and interplay between ostensibly diverse techniques.
Download or read book Beyond the Kalman Filter Particle Filters for Tracking Applications written by Branko Ristic and published by Artech House. This book was released on 2003-12-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most tracking applications the Kalman filter is reliable and efficient, but it is limited to a relatively restricted class of linear Gaussian problems. To solve problems beyond this restricted class, particle filters are proving to be dependable methods for stochastic dynamic estimation. Packed with 867 equations, this cutting-edge book introduces the latest advances in particle filter theory, discusses their relevance to defense surveillance systems, and examines defense-related applications of particle filters to nonlinear and non-Gaussian problems. With this hands-on guide, you can develop more accurate and reliable nonlinear filter designs and more precisely predict the performance of these designs. You can also apply particle filters to tracking a ballistic object, detection and tracking of stealthy targets, tracking through the blind Doppler zone, bi-static radar tracking, passive ranging (bearings-only tracking) of maneuvering targets, range-only tracking, terrain-aided tracking of ground vehicles, and group and extended object tracking.
Download or read book Handbook of Approximate Bayesian Computation written by Scott A. Sisson and published by CRC Press. This book was released on 2018-09-03 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the world becomes increasingly complex, so do the statistical models required to analyse the challenging problems ahead. For the very first time in a single volume, the Handbook of Approximate Bayesian Computation (ABC) presents an extensive overview of the theory, practice and application of ABC methods. These simple, but powerful statistical techniques, take Bayesian statistics beyond the need to specify overly simplified models, to the setting where the model is defined only as a process that generates data. This process can be arbitrarily complex, to the point where standard Bayesian techniques based on working with tractable likelihood functions would not be viable. ABC methods finesse the problem of model complexity within the Bayesian framework by exploiting modern computational power, thereby permitting approximate Bayesian analyses of models that would otherwise be impossible to implement. The Handbook of ABC provides illuminating insight into the world of Bayesian modelling for intractable models for both experts and newcomers alike. It is an essential reference book for anyone interested in learning about and implementing ABC techniques to analyse complex models in the modern world.
Download or read book Efficient Conditional Path Sampling of Stochastic Differential Equations written by Jonathan Quincy Weare and published by . This book was released on 2007 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
