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