How to Benefit from Noise

AbstractWe compare sequential and non-sequential designs for estimating linear functionals in the statistical setting, where experimental observations are contaminated by random noise. It is known that sequential designs are no better in the worst case setting for convex and symmetric classes, as well as in the average case setting with Gaussian distributions.In the statistical setting the opposite is true. That is, sequential designs can be significantly better. Moreover, by using sequential designs one can obtain much better estimators for noisy data than for exact data. In this way, problems that are computationally intractable for exact data may become tractable for noisy data. These results hold because adaptive observations and noise make it possible to simulate Monte Carlo