Probabilistic Forecasting and Bayesian Data AssimilationCambridge University Press, 14.05.2015 - 297 Seiten 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. |
Inhalt
Introduction to probability | 33 |
Computational statistics | 65 |
Stochastic processes | 96 |
Bayesian inference | 131 |
Basic data assimilation algorithms | 171 |
McKean approach to data assimilation | 200 |
Data assimilation for spatiotemporal processes | 229 |
Dealing with imperfect models | 259 |
A postscript | 288 |
| 295 | |
Andere Ausgaben - Alle anzeigen
Probabilistic Forecasting and Bayesian Data Assimilation Sebastian Reich,Colin Cotter Eingeschränkte Leseprobe - 2015 |
Probabilistic Forecasting and Bayesian Data Assimilation Sebastian Reich,Colin Cotter Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
4DVar analysis ensemble attractor averaged RMSE Bayesian inference Brownian dynamics Chapter coefficients computational consider convergence coupling covariance matrix data assimilation algorithms defined Definition denote deterministic discretisation discuss displayed in Figure dynamical system EnKF with perturbed ensemble inflation ensemble Kalman filter ensemble members ensemble prediction ensemble sizes ESRF estimate ETPF Example forecast ensemble formula forward operator function Gaussian random variable given Hence imperfect model implementation importance sampling independent initial conditions interval iteration leads localisation Lorenz-96 model marginal PDFs Markov chain Markov process mathematical mean zero measurement errors mechanistic model minimiser Monte Carlo methods Nobs numerical obtain optimal parameter particle filter perturbed observations prior quadrature rules realisations recursively reference solution rejection sampling resampling RMSEs sequence SIR filter spatial step-size stochastic process surrogate physical process tent map trajectory Tz(z uncertainty univariate vector yobs zn+1 zref(t