Probabilistic Forecasting and Bayesian Data Assimilation

Description

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. 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 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