Before revision:  Although designed for sampling from BayesCG posteriors, its mean and variance under approximate Krylov priors can be computed with CG. An approximation of the S-statistic by a `95 percent credible interval' avoids the cost of sampling altogether .  Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .
After revision:  Although designed for sampling from BayesCG posteriors, its mean and variance under approximate Krylov priors can be computed with CG. An approximation of the S-statistic by a `95 percent credible interval' avoids the cost of sampling altogether . This allows easy generation of accurate samples to probe uncertainty in subsequent computations. Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .