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In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for graduate students in applied mathematics, computer science, engineering, geoscience and other emerging application areas.Read more
- Opens up the subject for non-mathematicians working in any field where Bayesian data assimilation is applied
- Provides a novel unifying framework for ensemble-based data assimilation techniques
- MATLAB code is available to download from www.cambridge.org/9781107069398
Reviews & endorsements
'… an ideal platform for capstone experiences tailored to students with interests spanning applied mathematics and statistics.' D. V. Feldman, ChoiceSee more reviews
'Looking at it again from the mathematician's viewpoint, this is a beautiful articulation of the deep fact that methods which were originally developed to solve specific problems, and to get around specific issues, can be reformulated as special instances of a general theory. This book by Reich and Cotter thus makes an important and potentially very influential contribution to the literature. It is arguably most exciting in that the perspective promises to produce more and better algorithms. What more could one ask of a mathematical theory?' Christopher Jones, SIAM Review
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- Date Published: May 2015
- format: Paperback
- isbn: 9781107663916
- length: 308 pages
- dimensions: 244 x 170 x 16 mm
- weight: 0.61kg
- contains: 70 b/w illus. 7 colour illus. 70 exercises
- availability: Available
Table of Contents
1. Prologue: how to produce forecasts
Part I. Quantifying Uncertainty:
2. Introduction to probability
3. Computational statistics
4. Stochastic processes
5. Bayesian inference
Part II. Bayesian Data Assimilation:
6. Basic data assimilation algorithms
7. McKean approach to data assimilation
8. Data assimilation for spatio-temporal processes
9. Dealing with imperfect models
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