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In this paper, extensions to conventional stochastic estimation techniques are presented, whereby uncertainties in individual estimates may be deduced. Test applications to time series of velocity measurements in a turbulent boundary layer confirm the fidelity of the uncertainty estimation procedure and illustrate how the optimal choice of stochastic estimation model can be strongly dependent on the event upon which the average is conditioned. They also demonstrate how stochastic estimations may be refined to yield more accurate descriptions of particular coherent motions, and how they can reveal the existence of rare events, different in statistical character to their more frequent counterparts, which might otherwise be undetected by conventional stochastic estimation

Stochastic estimation as a statistical tool for approximating turbulent conditional averages