Description
Book SynopsisIn 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
Trade Review'… an ideal platform for capstone experiences tailored to students with interests spanning applied mathematics and statistics.' D. V. Feldman, Choice
'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
Table of ContentsPreface; 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.
