I have just uploaded a preprint of “Comments on the article ‘A Bayesian conjugate gradient method’” to the arXiv. This note discusses the recent paper “A Bayesian conjugate gradient method” in Bayesian Analysis by Jon Cockayne, Chris Oates, Ilse Ipsen, and Mark Girolami, and is an invitation to a rejoinder from the authors.
Abstract. The recent article “A Bayesian conjugate gradient method” by Cockayne, Oates, Ipsen, and Girolami proposes an approximately Bayesian iterative procedure for the solution of a system of linear equations, based on the conjugate gradient method, that gives a sequence of Gaussian/normal estimates for the exact solution. The purpose of the probabilistic enrichment is that the covariance structure is intended to provide a posterior measure of uncertainty or confidence in the solution mean. This note gives some comments on the article, poses some questions, and suggests directions for further research.