Prediction intervals to account for uncertainties in neural network predictions: Methodology and application in bus travel time prediction

Neural networks have been employed in a multitude of transportation engineering applications because of their powerful capabilities to replicate patterns in field data. Predictions are always subject to uncertainty arising from two sources: model structure and training data. For each prediction point, the former can be quantified by a confidence interval, whereas total prediction uncertainty can be represented by constructing a prediction interval. While confidence intervals are well known in the transportation engineering context, very little attention has been paid to construction of prediction intervals for neural networks. The proposed methodology in this paper provides a foundation for constructing prediction intervals for neural networks and quantifying the extent that each source of uncertainty contributes to total prediction uncertainty. The application of the proposed methodology to predict bus travel time over four bus route sections in Melbourne, Australia, leads to quantitative decomposition of total prediction uncertainty into the component sources. Overall, the results demonstrate the capability of the proposed method to provide robust prediction intervals.