Non-Gaussian Posteriors arising from Marginal Detections

Details Non-Gaussian Posteriors arising from Marginal Detections Non-Gaussian Posteriors arising from Marginal Detections

2010-05-10

arxiv.org/abs/1005.1664v2

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

13 pages, 7 figures, includes extended discussion of the implications of Non-Gaussianity from marginal detections, along with

Scientific paper

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.

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