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Mathematics > Numerical Analysis

arXiv:2208.03885 (math)
[Submitted on 8 Aug 2022]

Title:Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG

Authors:Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne, Chris J. Oates
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Abstract:We analyse the calibration of BayesCG under the Krylov prior, a probabilistic numeric extension of the Conjugate Gradient (CG) method for solving systems of linear equations with symmetric positive definite coefficient matrix. Calibration refers to the statistical quality of the posterior covariances produced by a solver. Since BayesCG is not calibrated in the strict existing notion, we propose instead two test statistics that are necessary but not sufficient for calibration: the Z-statistic and the new S-statistic. We show analytically and experimentally that under low-rank approximate Krylov posteriors, BayesCG exhibits desirable properties of a calibrated solver, is only slightly optimistic, and is computationally competitive with CG.
Comments: 40 Pages
Subjects: Numerical Analysis (math.NA)
MSC classes: 65F10, 62F15, 15A06
Cite as: arXiv:2208.03885 [math.NA]
  (or arXiv:2208.03885v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2208.03885

Submission history

From: Tim Reid [view email]
[v1] Mon, 8 Aug 2022 02:56:54 UTC (540 KB)
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