Using the maximum likelihood method, a formalism is derived to analyze a series of biased Monte Carlo or molecular dynamics simulations. The formalism is applied to different examples, in particular the estimation of thermodynamic properties of molecular systems such as potentials of mean force and free energy differences. The formalism is shown to be a generalization of existing methods that are known to be efficient. For the derivation, it is assumed that the values of the distribution function of subsequent states that are analyzed are uncorrelated.