2010/05/10 by Bassett, Bruce A., Afshordi, Niayesh
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.1005.1664
We show that in cases of marginal detections (~ 3σ), such as that of Baryonic Acoustic Oscillations (BAO) in cosmology, the often-used Gaussian approximation to the full likelihood is very poor, especially beyond ~3σ. This can radically alter confidence intervals on parameters and implies that one cannot naively extrapolate 1σ-errorbars to 3σ, 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.