  We review the introduction of likelihood functions and Fisher information in
classical estimation theory, and we show how they can be defined in a very
similar manner within quantum measurement theory. We show that the stochastic
master equations describing the dynamics of a quantum system subject to a
definite set of measurements provides likelihood functions for unknown
parameters in the system dynamics, and we show that the estimation error, given
by the Fisher information, can be identified by stochastic master equation
simulations. For large parameter spaces we describe and illustrate the
efficient use of Markov Chain Monte Carlo sampling of the likelihood function.
