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 . Numerical experiments confirm the effectiveness of the posteriors and their low-rank approximations .