A new Bayesian estimation framework for statistical feature extraction in the form of cepstral enhancement is presented, in which the joint prior distribution is exploited for both static and frame-differential dynamic cepstral parameters in the clean speech model. The conditional minimum mean square error (MMSE) estimator for the clean speech feature is derived using the full posterior probability for clean speech given the noisy observation. The final form of the estimator (for each mixture component) is a weighted sum of the prior information using the static and the dynamic priors separately, and of the prediction using the acoustic distortion model in absence of any prior information. Comprehensive noiserobust speech recognition experiments using the Aurora2 database demonstrate significant improvement in accuracy by incorporating the joint prior, compared with using only the static or dynamic prior and with using no prior.