Cockayne J

Ipsen ICF

Oates CJ

Reid TW

\ua9 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. We analyse the calibration of BayesCG under the Krylov prior. BayesCG is a probabilistic numeric extension of the Conjugate Gradient (CG) method for solving systems of linear equations with real symmetric positive definite coefficient matrix. In addition to the CG solution, BayesCG also returns a posterior distribution over the solution. In this context, a posterior distribution is said to be ‘calibrated’ if the CG error is well-described, in a precise distributional sense, by the posterior spread. Since it is known that BayesCG is not calibrated, we introduce two related weaker notions of calibration, whose departures from exact calibration can be quantified. Numerical experiments confirm that, under low-rank approximate Krylov posteriors, BayesCG is only slightly optimistic and exhibits the characteristics of a calibrated solver, and is computationally competitive with CG

Statistical properties of BayesCG under the Krylov prior

Abstract

Similar works

Full text

Available Versions

Newcastle University E-Prints