Valid Statistical Inference Based on Feedforward Artificial Neural Network Models

Janette F. Walde

Abstract

With the help of recent theoretical results, we use the estimates from neural network modelling as basis for formal statistical inference. Multi-layer perceptrons are applied to model biomass in a complex alpine terrain with limited amount of variables by combining temporal remote sensing with classical field methods from plant physiology. We test the hypothesis that the dynamics of the biomass distribution can be captured with the help of geo-registered and ortho-rectified colour images from the opposing hill slope. Therefore the network model is trained carefully and misspecification is tested by the non-linearity tests of Ramsey and of Teraesvirta, Lin and Granger. Plausibility and sensitivity analysis as well as ecological considerations in respect of content support the validity of our final model. With the help of bootstrap techniques the significance of colour patterns for modelling phytomass is demonstrated.