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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Certified dimension reduction in nonlinear Bayesian inverse problems
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by Olivier Zahm, Tiangang Cui, Kody Law, Alessio Spantini and Youssef Marzouk HTML | PDF
Math. Comp. 91 (2022), 1789-1835 Request permission


We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map which depends nontrivially only on a few linear combinations of the parameters. We build this ridge approximation by minimizing an upper bound on the Kullback–Leibler divergence between the posterior distribution and its approximation. This bound, obtained via logarithmic Sobolev inequalities, allows one to certify the error of the posterior approximation. Computing the bound requires computing the second moment matrix of the gradient of the log-likelihood function. In practice, a sample-based approximation of the upper bound is then required. We provide an analysis that enables control of the posterior approximation error due to this sampling. Numerical and theoretical comparisons with existing methods illustrate the benefits of the proposed methodology.
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Additional Information
  • Olivier Zahm
  • Affiliation: Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
  • MR Author ID: 1106417
  • ORCID: 0000-0003-1410-2940
  • Email:
  • Tiangang Cui
  • Affiliation: School of Mathematics, Monash University, Victoria 3800, Australia
  • MR Author ID: 1084083
  • ORCID: 0000-0002-4840-8545
  • Email:
  • Kody Law
  • Affiliation: School of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom
  • MR Author ID: 869711
  • Email:
  • Alessio Spantini
  • Affiliation: Center for Computational Science & Engineering, MIT, Cambridge, Massachusetts 02139
  • MR Author ID: 1084144
  • Email:
  • Youssef Marzouk
  • Affiliation: Center for Computational Science & Engineering, MIT, Cambridge, Massachusetts 02139
  • MR Author ID: 761311
  • Email:
  • Received by editor(s): January 27, 2021
  • Received by editor(s) in revised form: November 8, 2021, and January 18, 2022
  • Published electronically: April 27, 2022
  • Additional Notes: The first, third, fourth, and fifth authors were supported by the DARPA Enabling Quantification of Uncertainty in Physical Systems (EQUiPS) program, F. Fahroo and J. Vandenbrande, program managers, and by the Inria associate team UNQUESTIONABLE. The third author was also supported by the Oak Ridge National Laboratory Directed Research and Development program and by The Alan Turing Institute under the EPSRC grant EP/N510129/1. The second author was supported by the Australian Research Council under the grant DP210103092. The first and second authors were supported by the Robert Bartnik Fellowship offered by the School of Mathematics at Monash University.
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 1789-1835
  • MSC (2020): Primary 62C10, 91G60, 41-02
  • DOI:
  • MathSciNet review: 4435948