Bayesian Parameter Estimation via Filtering and Functional   Approximations
  The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations. 
Hermann G. Matthies, Alexander Litvinenko, Bojana V. Rosic, Elmar   Zander
math.NA math.PR