Paper Info
Title
Confidence Intervals for Stochastic Arithmetic
Abstract
AbstractQuantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It exists in different flavors, such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo, or Verrou. These methodologies and tools are based on the idea that FP losses of accuracy can be modeled via randomness. Therefore, they share the same need to perform a statistical analysis of programs results to estimate the significance of the results.In this article, we propose a framework to perform a solid statistical analysis of Stochastic Arithmetic. This framework unifies all existing definitions of the number of significant digits (CESTAC and MCA), and also proposes a new quantity of interest: the number of digits contributing to the accuracy of the results. Sound confidence intervals are provided for all estimators, both in the case of normally distributed results, and in the general case. The use of this framework is demonstrated by two case studies of industrial codes: Europlexus and code_aster.
Year
DOI
Venue
2018
10.1145/3432184
ACM Transactions on Mathematical Software
Keywords
Field
DocType
Stochastic arithmetic, Monte Carlo Arithmetic, numerical analysis, confidence intervals
Stochastic arithmetic,Aster (genus),Mathematical optimization,Uncertainty quantification,Algorithm,Confidence interval,Mathematics,Estimator,Randomness,Statistical analysis
Journal
Volume
Issue
ISSN
47
2
0098-3500
Citations 
PageRank 
References 
0
0.34
0
Authors
6
Name
Order
Citations
PageRank
Devan Sohier100.34
Pablo de Oliveira Castro2436.65
François Févotte311.04
Bruno Lathuilière421.81
Eric Petit55812.73
Olivier Jamond600.34