This paper provides a summary of our recent work on robust speech recognition based on a new statistical approach - the probabilistic union model. In particular, we considered speech recognition involving partial corruption in frequency bands, in time duration, and further in feature components. In all these situations, we assumed no prior knowledge about the corrupting noise, e.g. its band location, occurring time and statistical distribution. The new model characterizes these partial, unknown corruptions based on the union of random events. For the evaluation, we have conducted isolated-word recognition tasks by using both a speaker-independent E-set database and the TiDigits database, each being corrupted by various types of additive noise with unknown, time-varying statistics. The results indicate that the probabilistic union model offers robustness to partial corruption in speech utterances, requiring little or no knowledge about the noise characteristics.