This paper presents an in-depth study of classification of transients in power systems using two pattern classification methods, namely the maximum-likelihood, and the probabilistic neural networks. These methods, which stem from the Bayes rule, aim at estimating the underlying probability density functions that are required by the Bayes rule, but are often unavailable readily. The paper presents the mathematical foundations of classification using these two methods, followed by their implementation for classification of three types of transients, namely three-phase faults, breaker operations and capacitor switchings. Features used in this study are obtained using the wavelet and multifractal analyses of transient waveforms.