We develop,in the context of discriminantanalysis,a generalapproachto the designof neuralarchitectures. It consistsin building a neuralnet ‘around’a statistical model family; larger networks, made up of such elementarynetworks,arethen constructed.It is shown that, on the one hand, the statistical modeling approachprovidesa systematicway to obtaininggood approximationsin the neural network context, while, on the other, neural networks offer a powerful expansion to classical model families. A novel integrated approach emerges, which stressesboth flexibility (contribution of neural nets) and interpretability (contribution of statistical modeling). A well known data set on birth weight is analyzedby this new approach.The results are rather promising andopenthe way to manypotentialapplications.