Sampling the posterior: An approach to non-Gaussian data assimilation

摘要: The viewpoint taken in this paper is that data assimilation fundamentally a statistical problem and should be cast Bayesian framework. In the absence of model error, correct solution to find posterior distribution implied by setting. Methods for dealing with then judged their ability probe distribution. we propose range techniques probing distribution, based around Langevin equation; compare these new existing methods. When underlying dynamics deterministic, on space initial conditions leading sampling over space. When stochastic continuous time paths. By writing down density, conditioning observations, it possible define Markov Chain Monte Carlo (MCMC) methods which sample from desired thereby solve problem. basic building-blocks MCMC concentrate are equations ergodic whose invariant measures give distribution; case path partial differential (SPDEs). Two examples given show how can formulated fashion. first weather prediction, second Lagrangian oceanic velocity fields. Furthermore relationship between approach outlined here commonly used Kalman filter techniques, prevalent practice, discussed. Two simple pedagogical studied illustrate application concretely. Finally open mathematical computational issues, arising approach, outlined.