Aspects of network training and validation on noisy data: Part 2. Validation aspects

This paper focuses on the validation of multi-layered feed-forward (MLF) neural network models with respect to the predictive ability. Two distinct approaches for the computation of prediction intervals on neural network outputs have been applied and compared using simulated and experimental data. First, bootstrap resampling methodology has been applied and the results are discussed. The use of resampling techniques for variance estimation of network outputs is conveniently facilitated by means of the efficient Levenberg–Marquardt training method, as discussed in Part 1 of this paper. Next, the delta method, based on the linearization of nonlinear functions, has been applied and discussed. The bootstrap and the delta method are used to construct prediction intervals on neural network estimates. Finally, some practical aspects are outlined for both methods and some major conclusions are drawn.