Neural computing has emerged as a practical and powerful tool for "nonlinear" multivariate statistical analysis. In this paper, nonlinear discriminant analysis using a neural network is considered and applied to a medical diagnosis problem. The probabilistic interpretation of the network output is discussed in classification problems. The principle of the likelihood in network models is employed based on a probabilistic approach regarding the connection weights of the network as unknown parameters, and the maximum likelihood estimators of outputs are also introduced. Additionally, statistical techniques are formulated in terms of the principle of the likelihood of network models. The statistical tools for the inference illustrated here include i) deviance to evaluate the goodness-of-fit of a network model, ii) selection of the best fit model among several competing network models, and iii) likelihood-ratio chi-square statistics for pruning of neural network parameters and selection of a "best" subset of predictor variables.
