Sequential Optimal Inference For Experiments With Bayesian Particle Filters
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| Author | : Remi Daviet |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 2019 |
| Genre | : |
| ISBN | : |
In behavioral experiments, carefully choosing the stimuli is critical for success. Recently, several "adaptive" Bayesian methods gained popularity by proposing to optimally select the stimulus in each trial based on the results of the preceding trials. However, current methods are computationally expensive and might require a long waiting period between each question. Moreover, they are often tailored to a particular model and a particular objective, such as parameter estimation, prediction or model selection. It is left to the researcher to extend these approaches to other models by providing a suitable Bayesian inference method. We propose to apply the Sequential Monte Carlo (SMC) framework to solve both the inference problem and the optimal experimental design problem. This new method, called Sequential Optimal Inference (SOI) provides gains in computational efficiency and allows for the use of a broad class of complex models and objectives. We demonstrate its validity with simulation studies. An implementation of the method in MATLAB and Python is provided.
| Author | : Nicolas Chopin |
| Publisher | : Springer Nature |
| Total Pages | : 378 |
| Release | : 2020-10-01 |
| Genre | : Mathematics |
| ISBN | : 3030478459 |
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.
| Author | : Branko Ristic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 184 |
| Release | : 2013-04-15 |
| Genre | : Technology & Engineering |
| ISBN | : 1461463165 |
This book discusses state estimation of stochastic dynamic systems from noisy measurements, specifically sequential Bayesian estimation and nonlinear or stochastic filtering. The class of solutions presented in this book is based on the Monte Carlo statistical method. Although the resulting algorithms, known as particle filters, have been around for more than a decade, the recent theoretical developments of sequential Bayesian estimation in the framework of random set theory have provided new opportunities which are not widely known and are covered in this book. This book is ideal for graduate students, researchers, scientists and engineers interested in Bayesian estimation.
| Author | : Michael C. Burkhart |
| Publisher | : ProQuest Dissertations Publishing |
| Total Pages | : 134 |
| Release | : 2019-05-26 |
| Genre | : Mathematics |
| ISBN | : |
Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes’ rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein—von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant “T9” used the DKF to type out messages on a tablet PC. Nonstationarities, or changes to the statistical relationship between states and measurements that occur after model training, pose a significant challenge to effective filtering. In brain-computer interfaces, one common type of nonstationarity results from wonkiness or dropout of a single neuron. We show how a robust measurement model can be used within the DKF framework to effectively ignore large changes in the behavior of a single neuron. At BrainGate2, a successful online human neural decoding experiment validated this approach against the commonly-used Kalman filter.
| Author | : Simo Särkkä |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2013-09-05 |
| Genre | : Computers |
| ISBN | : 110703065X |
A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
| Author | : Arnaud Doucet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 590 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475734379 |
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.
| Author | : Lawrence D. Stone |
| Publisher | : Springer Nature |
| Total Pages | : 124 |
| Release | : 2023-05-31 |
| Genre | : Computers |
| ISBN | : 3031322428 |
This book provides a quick but insightful introduction to Bayesian tracking and particle filtering for a person who has some background in probability and statistics and wishes to learn the basics of single-target tracking. It also introduces the reader to multiple target tracking by presenting useful approximate methods that are easy to implement compared to full-blown multiple target trackers. The book presents the basic concepts of Bayesian inference and demonstrates the power of the Bayesian method through numerous applications of particle filters to tracking and smoothing problems. It emphasizes target motion models that incorporate knowledge about the target’s behavior in a natural fashion rather than assumptions made for mathematical convenience. The background provided by this book allows a person to quickly become a productive member of a project team using Bayesian filtering and to develop new methods and techniques for problems the team may face.
| Author | : Yinan Huang |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
A central theme in applied and computational statistics is the accurate and efficient methods of inference. The Bayesian paradigm performs inference based on the posterior distribution of unknown quantities. Throughout decades, there has been an enormous literature on computational Bayesian methods. Practical implementations, while succussful to different degrees, usually impose certain restrictions on the specific model structure. As more applications rely on complex model dynamics, more challenges remain to tackle the curse of high dimensionality and the analytical intractability of many non-Gaussian distributions. This thesis builds on existing research in the field of sequential Bayesian estimation for a general class of state-space models. We establish recursive Bayesian simulation algorithms to estimate parameters and states for a variety of diffusion and jump stochastic models. Our main work and contribution are two-fold. First, we build a particle filter framework for Levy-type state-space models. Particle filters are efficient numerical simulation techniques ideally suitable for highly nonlinear models, with a significant computational advantage over the standard Markov Chain Monte Carlo. Our particle filters can effectively estimate parameters and state variables for non-Gaussian dynamics. We perform empirical testing on financial time series, and find that certain Levy-type small jump processes can be a substitute of the usual Brownian motion-based random walk models. In addition, we propose a general Variational Bayes Particle Filter framework. It is applicable to a wider class of models with a large number of dimensions. Secondly, we build a Variational Bayes estimator for Hidden Markov Models with observational jumps. This is a typical setup for numerous biostatistical data analysis, where huge amounts of streaming data need to be sequentially filtered for potential evidence of the existence of quantitative traits or genetic features. Our algorithm works to identify and classify different responses. The hidden Markov estimator is robust and highly adaptable. In addition, this thesis also includes a self-contained chapter on the technique of Markovian projection. It reduces a complicated multi-dimensional dynamics to a one-dimensional simple Markovian process with identical marginal distributions, therefore keeping certain path-independent expectation values invariant. The projection has certain implications in the pricing of European-style options in financial mathematics. We provide a theorem generalizing existing results to the general Levy jump models, and discuss calibration issues.
| Author | : Peter Jan Van Leeuwen |
| Publisher | : Springer |
| Total Pages | : 130 |
| Release | : 2015-07-22 |
| Genre | : Mathematics |
| ISBN | : 3319183478 |
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
| Author | : James V. Candy |
| Publisher | : John Wiley & Sons |
| Total Pages | : 404 |
| Release | : 2011-09-20 |
| Genre | : Science |
| ISBN | : 1118210549 |
New Bayesian approach helps you solve tough problems in signal processing with ease Signal processing is based on this fundamental concept—the extraction of critical information from noisy, uncertain data. Most techniques rely on underlying Gaussian assumptions for a solution, but what happens when these assumptions are erroneous? Bayesian techniques circumvent this limitation by offering a completely different approach that can easily incorporate non-Gaussian and nonlinear processes along with all of the usual methods currently available. This text enables readers to fully exploit the many advantages of the "Bayesian approach" to model-based signal processing. It clearly demonstrates the features of this powerful approach compared to the pure statistical methods found in other texts. Readers will discover how easily and effectively the Bayesian approach, coupled with the hierarchy of physics-based models developed throughout, can be applied to signal processing problems that previously seemed unsolvable. Bayesian Signal Processing features the latest generation of processors (particle filters) that have been enabled by the advent of high-speed/high-throughput computers. The Bayesian approach is uniformly developed in this book's algorithms, examples, applications, and case studies. Throughout this book, the emphasis is on nonlinear/non-Gaussian problems; however, some classical techniques (e.g. Kalman filters, unscented Kalman filters, Gaussian sums, grid-based filters, et al) are included to enable readers familiar with those methods to draw parallels between the two approaches. Special features include: Unified Bayesian treatment starting from the basics (Bayes's rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation techniques (sequential Monte Carlo sampling) Incorporates "classical" Kalman filtering for linear, linearized, and nonlinear systems; "modern" unscented Kalman filters; and the "next-generation" Bayesian particle filters Examples illustrate how theory can be applied directly to a variety of processing problems Case studies demonstrate how the Bayesian approach solves real-world problems in practice MATLAB notes at the end of each chapter help readers solve complex problems using readily available software commands and point out software packages available Problem sets test readers' knowledge and help them put their new skills into practice The basic Bayesian approach is emphasized throughout this text in order to enable the processor to rethink the approach to formulating and solving signal processing problems from the Bayesian perspective. This text brings readers from the classical methods of model-based signal processing to the next generation of processors that will clearly dominate the future of signal processing for years to come. With its many illustrations demonstrating the applicability of the Bayesian approach to real-world problems in signal processing, this text is essential for all students, scientists, and engineers who investigate and apply signal processing to their everyday problems.
