Error propagation

Error propagation estimates uncertainty in a calculated result from uncertainty in its measured inputs, using the calculation’s mathematical relationships.

Propagation of uncertainty: A framework for determining how uncertainty in input quantities affects uncertainty in a result. It is the broader framework that error-propagation methods implement.
Measurement uncertainty: A quantified doubt about the value assigned to a measured quantity. It supplies the input uncertainty that the calculation must carry forward.
Uncertainty budget: A documented accounting of uncertainty contributions to a measurement result. It records how each input contributes to the final propagated uncertainty.
Worst-case analysis: An assessment using the most adverse allowed input values to bound an outcome. It seeks a bound rather than a probabilistic standard uncertainty.
First-order Taylor approximation: A linear approximation of a function near a chosen point, based on its first derivatives. Derivatives estimate how small input changes alter a calculated result.
Standard uncertainty: An uncertainty expressed as a standard deviation. Propagation formulas commonly combine input uncertainties in standard-deviation form.
Measurement model: A mathematical relationship connecting measured input quantities to a reported result. Its equation determines which uncertainties and dependencies enter the calculation.
Interval arithmetic: Arithmetic performed on intervals to enclose possible values of calculated quantities. It tracks value ranges instead of combining statistical uncertainty estimates.
Sensitivity analysis: The study of how changes in model inputs affect its outputs. Sensitivity identifies which uncertain inputs contribute most to the result’s uncertainty.
Measurement error: The difference between a measured value and the corresponding true quantity value. Error is a realized discrepancy; uncertainty describes the doubt surrounding a result.

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