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Bayesian Filtering and Smoothing

Bayesian Filtering and Smoothing Author Simo Särkkä
ISBN-10 9781107030657
Release 2013-09-05
Pages 254
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A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Bayesian Estimation and Tracking

Bayesian Estimation and Tracking Author Anton J. Haug
ISBN-10 9781118287804
Release 2012-05-29
Pages 448
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A practical approach to estimating and tracking dynamic systems in real-worl applications Much of the literature on performing estimation for non-Gaussian systems is short on practical methodology, while Gaussian methods often lack a cohesive derivation. Bayesian Estimation and Tracking addresses the gap in the field on both accounts, providing readers with a comprehensive overview of methods for estimating both linear and nonlinear dynamic systems driven by Gaussian and non-Gaussian noices. Featuring a unified approach to Bayesian estimation and tracking, the book emphasizes the derivation of all tracking algorithms within a Bayesian framework and describes effective numerical methods for evaluating density-weighted integrals, including linear and nonlinear Kalman filters for Gaussian-weighted integrals and particle filters for non-Gaussian cases. The author first emphasizes detailed derivations from first principles of eeach estimation method and goes on to use illustrative and detailed step-by-step instructions for each method that makes coding of the tracking filter simple and easy to understand. Case studies are employed to showcase applications of the discussed topics. In addition, the book supplies block diagrams for each algorithm, allowing readers to develop their own MATLAB® toolbox of estimation methods. Bayesian Estimation and Tracking is an excellent book for courses on estimation and tracking methods at the graduate level. The book also serves as a valuable reference for research scientists, mathematicians, and engineers seeking a deeper understanding of the topics.

Stochastic Processes and Filtering Theory

Stochastic Processes and Filtering Theory Author Andrew H. Jazwinski
ISBN-10 9780486318196
Release 2013-04-15
Pages 400
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This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.

Fundamentals of Stochastic Filtering

Fundamentals of Stochastic Filtering Author Alan Bain
ISBN-10 9780387768960
Release 2008-10-08
Pages 390
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This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.

Random Number Generation and Monte Carlo Methods

Random Number Generation and Monte Carlo Methods Author James E. Gentle
ISBN-10 9781475729603
Release 2013-03-14
Pages 247
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Monte Carlo simulation has become one of the most important tools in all fields of science. This book surveys the basic techniques and principles of the subject, as well as general techniques useful in more complicated models and in novel settings. The emphasis throughout is on practical methods that work well in current computing environments.

Beyond the Kalman Filter Particle Filters for Tracking Applications

Beyond the Kalman Filter  Particle Filters for Tracking Applications Author Branko Ristic
ISBN-10 1580538517
Release 2003-12-01
Pages 299
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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.

Bayesian Survival Analysis

Bayesian Survival Analysis Author Joseph G. Ibrahim
ISBN-10 9781475734478
Release 2013-03-09
Pages 480
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Survival analysis arises in many fields of study including medicine, biology, engineering, public health, epidemiology, and economics. This book provides a comprehensive treatment of Bayesian survival analysis. It presents a balance between theory and applications, and for each class of models discussed, detailed examples and analyses from case studies are presented whenever possible. The applications are all from the health sciences, including cancer, AIDS, and the environment.

Bayesian Reasoning and Machine Learning

Bayesian Reasoning and Machine Learning Author David Barber
ISBN-10 9780521518147
Release 2012-02-02
Pages 697
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A practical introduction perfect for final-year undergraduate and graduate students without a solid background in linear algebra and calculus.

Core Statistics

Core Statistics Author Simon Wood
ISBN-10 9781107071056
Release 2015-04-13
Pages 258
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Core Statistics is a compact starter course on the theory, models, and computational tools needed to make informed use of powerful statistical methods.

Bayesian Signal Processing

Bayesian Signal Processing Author James V. Candy
ISBN-10 9781119125488
Release 2016-06-20
Pages 640
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Presents the Bayesian approach to statistical signal processing for a variety of useful model sets This book aims to give readers a unified Bayesian treatment starting from the basics (Baye’s rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation model-based techniques (sequential Monte Carlo sampling). This next edition incorporates a new chapter on “Sequential Bayesian Detection,” a new section on “Ensemble Kalman Filters” as well as an expansion of Case Studies that detail Bayesian solutions for a variety of applications. These studies illustrate Bayesian approaches to real-world problems incorporating detailed particle filter designs, adaptive particle filters and sequential Bayesian detectors. In addition to these major developments a variety of sections are expanded to “fill-in-the gaps” of the first edition. Here metrics for particle filter (PF) designs with emphasis on classical “sanity testing” lead to ensemble techniques as a basic requirement for performance analysis. The expansion of information theory metrics and their application to PF designs is fully developed and applied. These expansions of the book have been updated to provide a more cohesive discussion of Bayesian processing with examples and applications enabling the comprehension of alternative approaches to solving estimation/detection problems. The second edition of Bayesian Signal Processing features: “Classical” Kalman filtering for linear, linearized, and nonlinear systems; “modern” unscented and ensemble Kalman filters: and the “next-generation” Bayesian particle filters Sequential Bayesian detection techniques incorporating model-based schemes for a variety of real-world problems Practical Bayesian processor designs including comprehensive methods of performance analysis ranging from simple sanity testing and ensemble techniques to sophisticated information metrics New case studies on adaptive particle filtering and sequential Bayesian detection are covered detailing more Bayesian approaches to applied problem solving MATLAB® notes at the end of each chapter help readers solve complex problems using readily available software commands and point out other software packages available Problem sets included to test readers’ knowledge and help them put their new skills into practice Bayesian Signal Processing, Second Edition is written for all students, scientists, and engineers who investigate and apply signal processing to their everyday problems.

Introduction to Malliavin Calculus

Introduction to Malliavin Calculus Author David Nualart
ISBN-10 9781107039124
Release 2018-09-30
Pages 246
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This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lvy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.

A First Course in Bayesian Statistical Methods

A First Course in Bayesian Statistical Methods Author Peter D. Hoff
ISBN-10 0387924078
Release 2009-06-02
Pages 272
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A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.

Probabilistic Robotics

Probabilistic Robotics Author Sebastian Thrun
ISBN-10 9780262201629
Release 2005-08-19
Pages 647
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Probablistic robotics is a growing area in the subject, concerned with perception and control in the face of uncertainty and giving robots a level of robustness in real-world situations. This book introduces techniques and algorithms in the field.

Asymptotic Statistics

Asymptotic Statistics Author A. W. van der Vaart
ISBN-10 0521784506
Release 2000-06-19
Pages 443
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A mathematically rigorous, practical introduction presenting standard topics plus research.

Lectures on the Poisson Process

Lectures on the Poisson Process Author Günter Last
ISBN-10 9781107088016
Release 2017-10-26
Pages 308
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A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

Transportation Statistics and Microsimulation

Transportation Statistics and Microsimulation Author Clifford Spiegelman
ISBN-10 9781439894545
Release 2016-04-19
Pages 384
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By discussing statistical concepts in the context of transportation planning and operations, Transportation Statistics and Microsimulation provides the necessary background for making informed transportation-related decisions. It explains the why behind standard methods and uses real-world transportation examples and problems to illustrate key concepts. The Tools and Methods to Solve Transportation Problems Classroom-tested at Texas A&M University, the text covers the statistical techniques most frequently employed by transportation and pavement professionals. To familiarize readers with the underlying theory and equations, it contains problems that can be solved using statistical software. The authors encourage the use of SAS’s JMP package, which enables users to interactively explore and visualize data. Students can buy their own copy of JMP at a reduced price via a postcard in the book. Practical Examples Show How the Methods Are Used in Action Drawing on the authors’ extensive application of statistical techniques in transportation research and teaching, this textbook explicitly defines the underlying assumptions of the techniques and shows how they are used in practice. It presents terms from both a statistical and a transportation perspective, making conversations between transportation professionals and statisticians smoother and more productive.

Bayesian Smoothing and Regression for Longitudinal Spatial and Event History Data

Bayesian Smoothing and Regression for Longitudinal  Spatial and Event History Data Author Ludwig Fahrmeir
ISBN-10 0199533024
Release 2011-04-28
Pages 544
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Bringing together recent advances in smoothing and semiparametric regression from a Bayesian perspective, this book demonstrates, with worked examples, the application of these statistical methods to a variety of fields including forestry, development economics, medicine and marketing.