The 2019 Q4 issue of SIAM Review will carry an article by Jon Cockayne, Chris Oates, Mark Girolami, and myself on the Bayesian formulation of probabilistic numerical methods, i.e. the interpretation of deterministic numerical tasks such as quadrature and the solution of ordinary and partial differential equations as (Bayesian) statistical inference tasks.
J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Bayesian probabilistic numerical methods.” SIAM Review 61(4):756–789, 2019.
Abstract. Over forty years ago average-case error was proposed in the applied mathematics literature as an alternative criterion with which to assess numerical methods. In contrast to worst-case error, this criterion relies on the construction of a probability measure over candidate numerical tasks, and numerical methods are assessed based on their average performance over those tasks with respect to the measure. This paper goes further and establishes Bayesian probabilistic numerical methods as solutions to certain inverse problems based upon the numerical task within the Bayesian framework. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well defined, encompassing both the nonlinear and non-Gaussian contexts. For general computation, a numerical approximation scheme is proposed and its asymptotic convergence established. The theoretical development is extended to pipelines of computation, wherein probabilistic numerical methods are composed to solve more challenging numerical tasks. The contribution highlights an important research frontier at the interface of numerical analysis and uncertainty quantification, and a challenging industrial application is presented.
The 2020 SIAM conference on Uncertainty Quantification (UQ20) will take place from 24 to 27 March 2020, on the Garching campus (near Munich) of the Technical University of Munich (TUM), Germany. UQ20 is being organised in cooperation with the GAMM Activity Group on UQ.
More information about the scientific programme will be added in due course, but the following scientists are already confirmed as plenary speakers:
- David M. Higdon, Virginia Polytechnic Institute and State University, USA
- George Em Karniadakis, Brown University, USA
- Frances Y. Kuo, University of New South Wales, Australia
- Youssef M. Marzouk, Massachusetts Institute of Technology, USA
- Anthony Nouy, École Centrale de Nantes, France
- Elaine Spiller, Marquette University, USA
- Claudia Tebaldi, The Joint Global Change Research Institute, USA
- Karen Veroy-Grepl, RWTH Aachen University, Germany
SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.
The fourth SIAM Conference on Uncertainty Quantification (SIAM UQ18) will take place at the Hyatt Regency Orange County, Garden Grove, California, this week, 16–19 April 2018.
As part of this conference, Mark Girolami, Philipp Hennig, Chris Oates and I will organise a mini-symposium on “Probabilistic Numerical Methods for Quantification of Discretisation Error” (MS4, MS17 and MS32).
The third SIAM Conference on Uncertainty Quantification (SIAM UQ16) will take place at the SwissTech Convention Center in Lausanne, Switzerland, this week, 5–8 April 2016.
As part of this conference, Mark Girolami and I will organise a mini-symposium on “Over-confidence in numerical predictions: challenges and solutions” (MS138 and MS153), which will feature a wide range of perspectives, including Bayesian and frequentist (in)consistency, probabilistic numerics, and application fields.