paper

Non-Gaussian Posteriors arising from Marginal Detections

arXiv:1005.1664

Abstract

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.

13 pages, 7 figures, includes extended discussion of the implications of Non-Gaussianity from marginal detections, along with explicit examples and an improved fitting formula to approximate the Non-Gaussian likelihood

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