How accurately can we measure the baryon acoustic oscillation feature?
  Baryon acoustic oscillations (BAO) represent one of the cleanest probes of
dark energy, allowing for tests of the cosmological model through the
measurement of distance and expansion rate from a 3D galaxy distribution. The
signal appears at large scales in the correlation function where linear theory
applies, allowing for the construction of accurate models. However, due to the
lower number of modes available at these scales, sample variance has a
significant impact on the signal, and may sharpen or widen the underlying peak.
Therefore, equivalent mock realizations of a galaxy survey present different
errors in the position of the peak when uncertainties are estimated from the
posterior probability distribution corresponding to the individual mocks. Hence
the posterior width, often quoted as the error in BAO survey measurements, is
subject to sample noise. A different definition of the error is provided by the
asymptotic variance of the maximum likelihood estimator, which involves the
average over multiple realizations, and is not subject to sample noise. In this
work we re-analyse the main galaxy survey data available for BAO measurements
and quantify the impact of the noise component on the error quoted for BAO
measurements. We quantify the difference between three definitions of the
error: the confidence region computed from a single posterior, the average of
the variances of many realizations, and the Fisher matrix prediction assuming a
Gaussian likelihood.
