Before revision:  Because of its factored form, the Krylov prior is amenable to low-rank approximation, which produces an efficient BayesCG implementation as a CG method. We also introduce a probabilistic error estimator, the `S-statistic'. 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:  Because of its factored form, the Krylov prior is amenable to low-rank and maintained in factored form . Numerical experiments illustrate that the resulting error estimates are competitive with the best existing methods and are easy to compute .