Abstract
Correlations play a significant role in data analysis and the evaluation and expression of the uncertainty, yet estimating them is often difficult. This paper provides examples of how to infer the measurand value, given only the uncertainties and correlation ranges of the measurement results. The least informative data-distribution is not Gaussian, but the marginal distributions are. Explicit results are given in the case of a data pair, where the inferred correlation coefficient is the midpoint of the given range.
Highlights
Correlations play an important role in data analysis and evaluating and expressing the uncertainty [1,2,3,4,5,6,7]
Correlations play a significant role in data analysis and the evaluation and expression of the uncertainty, yet estimating them is often difficult
This paper provides examples of how to infer the measurand value, given only the uncertainties and correlation ranges of the measurement results
Summary
Correlations play an important role in data analysis and evaluating and expressing the uncertainty [1,2,3,4,5,6,7]. We consider the evaluation of the least-informative distribution and correlation coefficient by considering a data. We determine the sought distribution by ensuring that, subject to any contextual information, it is minimally informative. In this way can we be sure that the distribution and correlation coefficient take all the information available into account, but no uncontrolled assumptions have been introduced. The maximum entropy principle, which minimizes the Shannon information encoded in a distribution, solves the problem.
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