Premium
Uncertainty quantification via codimension‐one partitioning
Author(s) -
Sullivan T. J.,
Topcu U.,
McKerns M.,
Owhadi H.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3030
Subject(s) - mathematics , context (archaeology) , measure (data warehouse) , upper and lower bounds , domain (mathematical analysis) , codimension , uncertainty quantification , probability measure , discrete mathematics , statistics , computer science , pure mathematics , mathematical analysis , paleontology , biology , database
We consider uncertainty quantification in the context of certification, i.e. showing that the probability of some ‘failure’ event is acceptably small. In this paper, we derive a new method for rigorous uncertainty quantification and conservative certification by combining McDiarmid's inequality with input domain partitioning and a new concentration‐of‐measure inequality. We show that arbitrarily sharp upper bounds on the probability of failure can be obtained by partitioning the input parameter space appropriately; in contrast, the bound provided by McDiarmid's inequality is usually not sharp. We prove an error estimate for the method (Proposition 3.2); we define a codimension‐one recursive partitioning scheme and prove its convergence properties (Theorem 4.1); finally, we apply a new concentration‐of‐measure inequality to give confidence levels when empirical means are used in place of exact ones (Section 5). Copyright © 2010 John Wiley & Sons, Ltd.