Predictions with Confidence Intervals (Local Error Bars)

We present a new method for obtaining local error bars, i.e., estimates of the confidence in the predicted value that depend on the input. We approach problem of nonlinear regression in a maximum likelihood framework. We demonstrate our technique first on computer generated data with locally varying, normally distributed target noise. We then apply it to the laser data from the Santa Fe Time Series Competition. Finally, we extend the technique to estimate error bars for iterate predictions, and apply it to the exact competition task where it gives the best performance to date.