Evaluating and communicating uncertainty in the presence of non-white noise

Classical uncertainty evaluation uses probability density functions that are both Gaussian and stationary in variance about a mean, which may be drifting. Uncertainty in the drift rate means the full uncertainty propagator must allow for the progressive growth of uncertainty as time passes after a calibration. Additionally, the variance is often unavoidably non-stationary: e.g. its within-group variance is less than its between-group variance. We illustrate how this non-stationarity can be studied by Fourier analysis. In many cases, in addition to classical white noise with its flat power spectrum of fluctuations, 1/f and/or 1/f² noise is revealed. A broad class of non-white noise models, that might be thought to give divergent results, is harnessed to derive its explicit uncertainty propagator to describe the growth of uncertainty with time. The propagator suggests simple ways for checking between-time variances for the presence of random walk noise.