Confidence regions for cascaded neural network prediction in power markets

Neural networks have been used in forecasting tasks. A key question is how accurate the predictions are. This is important since forecasting is usually used for decision making. Prediction quality can be quantified by the confidence regions, which are usually associated with the network output distribution or variance. The confidence region problem is difficult since the output distribution is complicated to derive. It is also hard to implement even if the distribution is derived. This paper presents a Bayesian inference framework that considers weight noise, measurement type input noise, and prediction stage input noise for cascaded neural network prediction. The distribution of the network output is approximated to be Gaussian and confidence regions are then obtained by deviating a certain number of standard deviations from the mean. An online confidence region algorithm independent on the network learning is also developed. This method is general and can be applied to various neural networks structures. Testing results on a nonlinear function composed of exponential terms and on market clearing price show that confidence regions are efficiently obtained, and provide valuable information for risk management