Sarle As posted to the several .stats groups. There is considerable overlap between the fields of neural networks and statistics.
Statistics is concerned with data analysis.
In neural network terminology, statistical inference means learning to generalize from noisy data. But most neural networks that can learn to generalize effectively from noisy data are similar or identical to statistical methods. Feedforward nets with one hidden layer are closely related to projection pursuit regression. Probabilistic neural nets are identical to kernel discriminant analysis. General regression neural nets are identical to Nadaraya-Watson kernel regression.