Probabilistic Forecasting and Bayesian Data Assimilation - Cotter, Colin

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Résumé :
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....

Biographie:
Sebastian Reich is Professor of Numerical Analysis at the University of Potsdam (full time) and the University of Reading (part time). He also holds an honorary visiting professorship at Imperial College London. Reich is the author of over 100 journal articles and the co-author of Simulating Hamiltonian Dynamics (Cambridge, 2005), which has received more than 600 citations. His research areas cover numerical analysis and scientific computing with applications to classical mechanics, molecular dynamics, geophysical fluid dynamics, and data assimilation. In 2003 he received the Germund Dahlquist Prize from the Society for Industrial and Applied Mathematics (SIAM) for his work on geometric integration methods.

Sommaire:
Preface; 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; References; Index.