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Computing the variance of a conditional expectation has often been ofimportance in uncertainty quantification. Sun et al. has introduced an unbiasednested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulationsince the optimal inner-level sample size is bounded as the computationalbudget increases. In this letter we construct unbiased non-nested Monte Carloestimators based on the so-called pick-freeze scheme due to Sobol'. Anextension of our approach to compute higher order moments of a conditionalexpectation is also discussed.

Computing the variance of a conditional expectation via non-nested Monte Carlo