How to optimally combine pre-reconstruction full shape and
  post-reconstruction BAO signals
  We review the different approaches for combining the cosmological information
from the full shape of the pre-reconstructed power spectrum - usually referred
as redshift-space distortion (RSD) analysis - and from the baryon acoustic
oscillation (BAO) peak position in the post-reconstructed power spectrum with
the aim of finding the optimal procedure. We focus on combining the pre- and
post-reconstructed derived quantities at different compression levels: 1) the
two-point summary statistics, the power spectrum multipoles, $P^{(\ell)}(k)$;
2) the compressed BAO variables, $\alpha_{\parallel,\perp}$; and 3) an hybrid
approach between 1) and 2). We apply these methods to the publicly available
eBOSS Luminous Red Galaxy catalogues, for both data and synthetic EZ-mocks. We
find that the three approaches result in very consistent posteriors when the
appropriate covariance matrix estimator is used. On average, the combination at
$P^{(\ell)}(k)$ level retrieves $5-10\%$ tighter constraints than the other two
approaches, demonstrating that the standard approach of combining at the level
of the BAO variables is nearly optimal. We conclude that combining both BAO
post-reconstructed and full shape pre-reconstructed signals for the one single
data realization at the level of the summary statistics is faster, as it does
not require running the whole pipeline on the individual mocks, and brings a
moderate $10\%$ improvement, with respect to the other two studied methods.
Moreover, we check for potential systematics, such as, the way the matrix is
built and the effect of the finite number of mocks on the likelihood estimator
and find none of these have a significant impact in the final results.
Combining the pre- and post-reconstruction signals at the level of the summary
statistics is an attractive, faster and accurate method to be used in future
and on-going spectroscopic surveys.
