  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.
