Nullwen: Upper Limit Statistics
Measurement, Noise & the Lab arc, page 129 of 193. Back to The Pixelated Physics Universe
Who they are
Nullwen has one line, and says it often: “Nothing found. 90% confident.”
Nullwen is a character of the Measurement, Noise & the Lab arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
An upper limit is a result: the Feldman–Cousins unified approach gives confidence intervals that move smoothly from upper limits to two-sided intervals.
$$ \begin{gathered} R = \frac{P(n \mid \mu)}{P(n \mid \mu_{\text{best}})} \\ P(n \mid \mu) = \frac{(\mu + b)^{n}\, e^{-(\mu + b)}}{n!} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $R$ | likelihood-ratio ordering variable | — |
| $n$ | observed number of events | — |
| $\mu$ | signal mean | — |
| $\mu_{\text{best}}$ | physically allowed μ that maximises P(n | μ) |
| $b$ | known mean background | — |
Sources
Crossovers
Nullwen meets Chivelle (Chi-Squared Goodness of Fit). Nullwen turns a non-detection into a precise upper limit. Chivelle checks that the fit behind it is honest: a χ²/ndf far below 1 means the error bars were inflated.
Nullwen meets Neutrina Fade (Neutrino Ghost Matter). Neutrina Fade's absolute mass is still unknown, but Nullwen's craft sets upper limits on it from experiments such as tritium beta decay.
Wear the lore
Concept keywords: Upper Limit Statistics, Nullwen, Measurement, Noise & the Lab, physics lore, Pixelated Physics