A gravitational-wave burst search pipeline runs five checks on its background triggers.
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Data analysis and model fitting in the laboratory
Error, Chance and the Machine, Ch Tests, intervals and Bayesian inference
Problem
A gravitational-wave burst search pipeline runs five checks on its background triggers.
((a)) A noise-only model is fitted to N=14 time-frequency bins with p=2 free parameters, giving χ2=15.0. Using Q(χ2;ν)=e−χ2/2∑i=0ν/2−1(χ2/2)i/i!, find ν and the p-value.
((b)) A single trigger's amplitude (standard deviation σ=1 in the search's ranking units) is used to test H0:μ=0 against H1:μ=1 at size α=0.05 (z0.05=1.645). Give the Neyman-Pearson threshold and its power, using Φ(0.645)=0.7405.
((c)) Freeing the chirp mass, which the simpler waveform fit holds at a value well inside its allowed range, gives −2lnΛ=16.0. Using Φ(4.0)=0.99997, find the p-value from Wilks' theorem.
((d)) No astrophysical trigger survives the veto in a search epoch whose background after the veto is negligible. Find the 80 per cent Neyman upper limit on the mean number of events.
((e)) Vetting runs in two batches: 18 of the first 20 background triggers and 27 of the next 30 are correctly classified as noise. With a uniform prior on the classification efficiency θ, give the posterior after the first batch, use it as the prior for the second batch, and check that the result is the posterior from all 50 at once. Give its mean and mode.