Error Bars on Predictions
A prediction without an error bar hides how much to trust it; sound surrogates report calibrated uncertainty alongside every value.
Why every prediction needs one
A single predicted number invites false confidence. An error bar - a standard deviation, a credible interval, or a full predictive distribution - states how much the prediction could plausibly be off. For any decision, the width of the error bar can matter more than the central value, because it governs risk.
Where the uncertainty comes from
- Input uncertainty propagated through the model
- Surrogate approximation error from limited or poorly placed training data
- Observation noise in the data the surrogate learned from
- Model-form error - the equations are imperfect
Surrogates that report it natively
Gaussian processes are the archetype: their predictive variance grows with distance from training points, giving a built-in error bar that is small near data and large in extrapolation. Bayesian methods generally produce full predictive distributions. This self-awareness is what makes such surrogates suitable for active learning and risk-aware design.
Adding error bars to deterministic surrogates
Neural networks and RBF interpolants give point predictions by default. Uncertainty is added by ensembling (train several models and use their spread), bootstrap resampling, Monte Carlo dropout, jackknife or conformal methods, or by training the model to output a variance as well as a mean. Without one of these, such a surrogate is silent about its own reliability.
Calibration matters
An error bar is only useful if it is honest: a stated ninety percent interval should contain the truth about ninety percent of the time. Overconfident intervals - too narrow - are dangerous because they hide risk. Calibration is checked on held-out data and corrected if the reported uncertainty does not match observed error frequencies.
Kronos practice
Every surrogate-based prediction for the machines carries an uncertainty estimate, and those estimates are validated for calibration. A simulated performance figure is always reported as a range with stated conditions, never as a bare number, and never presented as a measured hardware result before it exists.