The model training algorithm is a critical component in the statistical pattern recognition approaches which are based on the Bayes decision theory. Conventional applications of the Bayes decision theory usually assume uniform error cost and result in a ubiquitous use of the maximum a posteriori (MAP) decision policy and the paradigm of distribution estimation as practice in the design of a statistical pattern recognition system. The minimum classification error (MCE) training method is proposed to overcome some substantial limitations for the conventional distribution estimation methods. In this thesis, three aspects of the MCE method are generalized. First, an optimal classifier/recognizer design framework is constructed, aiming at minimizing non-uniform error cost.A generalized training criterion named weighted MCE is proposed for pattern and speech recognition tasks with non-uniform error cost. Second, the MCE method for speech recognition tasks requires appropriate management of multiple recognition hypotheses for each data segment. A modified version of the MCE method with a new approach to selecting and organizing recognition hypotheses is proposed for continuous phoneme recognition. Third, the minimum verification error (MVE) method for detection-based automatic speech recognition (ASR) is studied. The MVE method can be viewed as a special version of the MCE method which aims at minimizing detection/verification errors. We present many experiments on pattern recognition and speech recognition tasks to justify the effectiveness of our generalizations.