Nonlinear modeling with confidence estimation using Bayesian neural networks

There is a growing interest in the use of neural networks in civil engineering to model complicated nonlinearity problems. A recent enhancement to the conventional back-propagation neural network algorithm is the adoption of a Bayesian inference procedure that provides good generalization and a statistical approach to deal with data uncertainty. A review of the Bayesian approach for neural network learning is presented. One distinct advantage of this method over the conventional back-propagation method is that the algorithm is able to provide assessments of the confidence associated with the  network’s predictions. Two examples are presented to demonstrate the capabilities of this algorithm. A third example considers the practical application of the Bayesian neural network approach for analyzing the ultimate shear strength of deep beams.