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 \((\frac{\sigma_{a/b}}{a/b})^{2} = (\frac{\sigma_{a}}{a})^{2} + (\frac{\sigma_{b}}{b})^{2}\).