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We review the introduction of likelihood functions and Fisher information inclassical estimation theory, and we show how they can be defined in a verysimilar manner within quantum measurement theory. We show that the stochasticmaster equations describing the dynamics of a quantum system subject to adefinite set of measurements provides likelihood functions for unknownparameters in the system dynamics, and we show that the estimation error, givenby the Fisher information, can be identified by stochastic master equationsimulations. For large parameter spaces we describe and illustrate theefficient use of Markov Chain Monte Carlo sampling of the likelihood function.

Bayesian parameter inference from continuously monitored quantum systems