A probability distribution for speech model parameters, such as auto-regression parameters, is used to identify a distribution of denoised values from a noisy signal. Under one embodiment, the probability distributions of the speech model parameters and the denoised values are adjusted to improve a variational inference so that the variational inference better approximates the joint probability of the speech model parameters and the denoised values given a noisy signal. In some embodiments, this improvement is performed during an expectation step in an expectation-maximization algorithm. The statistical model can also be used to identify an average spectrum for the clean signal and this average spectrum may be provided to a speech recognizer instead of the estimate of the clean signal.