Propagation of uncertainties#

If present, scipp propagates uncertainties (errors) as described in Wikipedia: Propagation of uncertainty. The implemented mechanism assumes uncorrelated data.

An overview for key operations is:

Operation \(f\)

Variance \(\sigma^{2}_{f}\)

\(-a\)

\(\sigma^{2}_{a}\)

\(|a|\)

\(\sigma^{2}_{a}\)

\(\sqrt{a}\)

\(\frac{1}{4} \frac{\sigma^{2}_{a}}{a}\)

\(a + b\)

\(\sigma^{2}_{a} + \sigma^{2}_{b}\)

\(a - b\)

\(\sigma^{2}_{a} + \sigma^{2}_{b}\)

\(a * b\)

\(\sigma^{2}_{a}b^{2} + \sigma^{2}_{b}a^{2}\)

\(a / b\)

\(\frac{\sigma^{2}_{a} + \sigma^{2}_{b} \frac{a^{2}}{b^{2}}}{b^{2}}\)

\(e^{a}\)

\(e^{2a} \sigma^{2}_{a}\)

\(\log(a)\)

\(\sigma^{2}_{a} / a^{2}\)

\(\log_{10}(a)\)

\(\sigma^{2}_{a} \log^{2}(10) / a^{2}\)

The expression for division is derived from \((\frac{\sigma_{a/b}}{a/b})^{2} = (\frac{\sigma_{a}}{a})^{2} + (\frac{\sigma_{b}}{b})^{2}\).