Schematic of the detection inference. Given the data, d, which is the linear combination of the noise distribution, n, plus the signal, s, we can define the likelihood of detection ${\mathcal{L}}_{\mathrm{D}}(\gamma )$ by setting an arbitrary S/N threshold γ and integrating the probability density function of the S/N for d from γ to ∞, as indicated with the shaded area. By nullifying s through jackknifing of d, we recover the ideal thermal noise, n, and thus compute the likelihood of a false positive detection ${\mathcal{L}}_{\mathrm{F}\mathrm{D}}(\gamma )$ as we do for computing ${\mathcal{L}}_{\mathrm{D}}(\gamma )$. The ratio of the two likelihoods provides the significance of detection. This figure is inspired by Fig. 1 of Vio & Andreani (2016).