This paper investigates speech and speaker recognition involving partial feature corruption, assuming unknown, time-varying noise characteristics. The probabilistic union model is extended from a conditional-probability formulation to a posterior-probability formulation as an improved solution to the problem. The new formulation allows the order of the model to be optimized for every single frame, thereby enhancing the capability of the model for dealing with nonstationary noise corruption. The new formulation also allows the model to be readily incorporated into a Gaussian mixture model (GMM) for speaker recognition. Experiments have been conducted on two databases: TIDIGITS and SPIDRE, for speech recognition and speaker identification. Both databases are subject to unknown, time-varying band-selective corruption. The results have demonstrated the improved robustness for the new model.