Artificial Neural Networks as Non-Linear Extensions of Statistical Methods in Astronomy

We attempt to de-mistify Artificial Neural Networks (ANNs) by considering special cases which are related to other statistical methods common in Astronomy and other fields. In particular we show how ANNs generalise Bayesian methods, multi-parameter fitting, Principal Component Analysis (PCA), Wiener filtering and regularisation methods. Examples of morphological classification of galaxies illustrate how non-linear ANNs improve on linear techniques.