https://pseyfert.codeberg.page/tags/math/ Recent content in Math on Yet another blog restart Hugo en-us Tue, 22 Dec 2015 00:00:00 +0000 https://pseyfert.codeberg.page/2015/12/what-i-dont-like-about-binomial-errors-and-how-significant-is-the-performance-difference-of-two-bdts/ Tue, 22 Dec 2015 00:00:00 +0000 https://pseyfert.codeberg.page/2015/12/what-i-dont-like-about-binomial-errors-and-how-significant-is-the-performance-difference-of-two-bdts/ <p>A topic I already discussed in my master thesis is the determination of efficiencies, commonly denoted as \(\varepsilon=k/N\). Even assuming absolute certainty on \(k\) and \(N\) (that means: no fit is involved, it&rsquo;s just counting, the only uncertainty one would assume is the standard \(\sqrt(N)\) when referring to the uncertainty on a Poisson mean) the error propagation seems hard and is often done wrong. The naive propagation (relative error is quadratic sum of relative errors of \(k\) and \(N\)) is clearly wrong because it neglects the correlation of \(k\) and \(N\). Once realising this, one uses the so-called binomial error, \(\sqrt{\varepsilon * (1-\varepsilon)/N}\), which I also dislike.</p>