Many important problems in signal processing can be reduced to the selection of the parameters in a filtering structure. In this paper, we introduce a general selection criterion that relies on the ability to characterize the desired signal to be obtained at the filter output in terms of its probability density function (pdf). Using this statistical reference, the filter parameters are chosen in order to maximize the likelihood of the filtered signal under the desired probability distribution. We study the feasibility and asymptotic properties of this approach and present an illustrative simulation example, where the Space Alternating Generalized Expectation-maximization (SAGE) algorithm is used in the numerical implementation of the proposed method.