  We show that in cases of marginal detections (~ 3\sigma), such as that of
Baryonic Acoustic Oscillations (BAO) in cosmology, the often-used Gaussian
approximation to the full likelihood is very poor, especially beyond ~3\sigma.
This can radically alter confidence intervals on parameters and implies that
one cannot naively extrapolate 1\sigma-errorbars to 3\sigma, and beyond. We
propose a simple fitting formula which corrects for this effect in posterior
probabilities arising from marginal detections. Alternatively the full
likelihood should be used for parameter estimation rather than the Gaussian
approximation of a just mean and an error.
