Flyvbjerg and Petersen argue that the block-averaging method is cheaper than calculating the autocovariance function and avoids having to select the truncation point of the sum of autocovariance terms. However, using overlapping block averages provides a reduced variance variance estimate compared to non-overlapping block averages, and is equivalent to applying an appropriately sized Bartlett window to the autocovariance function. This clarifies that the problem of truncation point selection is not avoided by using a block averaging method; it is closely related to the issue of block size selection. Furthermore, the additional computational cost (which is likely negligible with modern hardware) can bring a reduced variance variance estimate. As discussed by Gowers et al., use of the autocovariance function is also easily automatable. In addition, methods we are aware of for estimating the optimal block size require calculating the autocovariance function as an intermediate step, making more direct use of the autocovariance function simpler. Therefore, calculating variance of the mean estimates using autocovariance function-based methods may be preferable. Using uncorrelated or window estimators (without determining a suitable window size based on the data) may substantially underestimate the variance of the mean due to the incomplete treatment of correlation. Of the initial sequence methods, Geyer's initial positive sequence method will often provide the smallest underestimate because it produces the latest truncation of the autocorrelation function. However, this will still systematically underestimate the variance of the mean, as noise in the autocorrelation function will result in early truncation (as negative Γ terms will appear earlier in the series with increasing noise).