The Library
Optimal uncertainty quantification for legacy data observations of Lipschitz functions
Tools
Sullivan, T. (2013) Optimal uncertainty quantification for legacy data observations of Lipschitz functions. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (Number 6). pp. 1657-1689. doi:10.1051/m2an/2013083 ISSN 0764-583X.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1051/m2an/2013083
Abstract
We consider the problem of providing optimal uncertainty quantification (UQ) – and hence rigorous certification – for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter sensitivities (McDiarmid diameters) and output deviation (or failure) probabilities. The solutions of these optimization problems depend non-trivially (even non-monotonically and discontinuously) upon the specified legacy data. Furthermore, the extreme values are often determined by only a few members of the data set; in our principal physically-motivated example, the bounds are determined by just 2 out of 32 data points, and the remainder carry no information and could be neglected without changing the final answer. We propose an analogue of the simplex algorithm from linear programming that uses these observations to offer efficient and rigorous UQ for high-dimensional systems with high-cardinality legacy data. These findings suggest natural methods for selecting optimal (maximally informative) next experiments.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | ESAIM: Mathematical Modelling and Numerical Analysis | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0764-583X | ||||
Official Date: | November 2013 | ||||
Dates: |
|
||||
Volume: | Volume 47 | ||||
Number: | Number 6 | ||||
Page Range: | pp. 1657-1689 | ||||
DOI: | 10.1051/m2an/2013083 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |