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Title: Experimental uncertainty estimation and statistics for data having interval uncertainty.

Abstract

This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute various means, the median and other percentiles, variance, interquartile range, moments, confidence limits, and other important statistics and summarizes the computability of these statistics as a function of sample size and characteristics of the intervals in the data (degree of overlap, size and regularity of widths, etc.). It also reviews the prospects for analyzing such data sets with the methods of inferential statistics such as outlier detection and regressions. The report explores the tradeoff between measurement precision and sample size in statistical results that are sensitive to both. It also argues that an approach based on interval statistics could be a reasonable alternative to current standard methods for evaluating, expressing and propagating measurement uncertainties.

Authors:
 [1];  [2];  [2];  [2];  [2]
  1. (Applied Biomathematics, Setauket, New York)
  2. (Applied Biomathematics, Setauket, New York)
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
910198
Report Number(s):
SAND2007-0939
TRN: US200723%%374
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DATA COVARIANCES; ALGORITHMS; STATISTICS; PROBABILISTIC ESTIMATION; DATA ANALYSIS; Statistics.; Uncertainty-Analysis.; Uncertainty-Mathematical models.

Citation Formats

Kreinovich, Vladik, Oberkampf, William Louis, Ginzburg, Lev, Ferson, Scott, and Hajagos, Janos. Experimental uncertainty estimation and statistics for data having interval uncertainty.. United States: N. p., 2007. Web. doi:10.2172/910198.
Kreinovich, Vladik, Oberkampf, William Louis, Ginzburg, Lev, Ferson, Scott, & Hajagos, Janos. Experimental uncertainty estimation and statistics for data having interval uncertainty.. United States. doi:10.2172/910198.
Kreinovich, Vladik, Oberkampf, William Louis, Ginzburg, Lev, Ferson, Scott, and Hajagos, Janos. Tue . "Experimental uncertainty estimation and statistics for data having interval uncertainty.". United States. doi:10.2172/910198. https://www.osti.gov/servlets/purl/910198.
@article{osti_910198,
title = {Experimental uncertainty estimation and statistics for data having interval uncertainty.},
author = {Kreinovich, Vladik and Oberkampf, William Louis and Ginzburg, Lev and Ferson, Scott and Hajagos, Janos},
abstractNote = {This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute various means, the median and other percentiles, variance, interquartile range, moments, confidence limits, and other important statistics and summarizes the computability of these statistics as a function of sample size and characteristics of the intervals in the data (degree of overlap, size and regularity of widths, etc.). It also reviews the prospects for analyzing such data sets with the methods of inferential statistics such as outlier detection and regressions. The report explores the tradeoff between measurement precision and sample size in statistical results that are sensitive to both. It also argues that an approach based on interval statistics could be a reasonable alternative to current standard methods for evaluating, expressing and propagating measurement uncertainties.},
doi = {10.2172/910198},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}

Technical Report:

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