stats.tex

\section{Statistical Methods}
\label{sec:stats}


LSST will generate very large galaxy samples that can be used for
investigations of the galaxy distribution -- e.g. correlation
functions, luminosity functions, dependence on environment -- that are
much more sensitive than what we are used to. These will enable
measurement of features and evolution at high precision. At the same
time, these samples will largely rely on photometric redshifts. To
take full advantage, and to avoid introducing subtle systematics,
astronomers will have to develop methods that use the full information
in the photo-z P(z) estimate, rather than using point estimates
(placing galaxies at their best estimate redshift).

This will require developing techniques for probabilistic inference
over photo-z probability distributions, when measuring typical
population estimates such as the luminosity function or correlation
function. It will generally not be practical to forward-model the
entire dataset (e.g. constraining the luminosity function directly
from galaxy apparent magnitudes, in principle would require modeling
the LF and colors of all galaxies at all redshifts). So investigators
will use photo-z probability distributions calculated either by the
LSST pipeline or their own.  Generalizing the standard measurements to
use the information in the P(z) distribution and to be robust against
errors in estimating P(z) is a relatively unexplored area. Simple
ideas such as randomly sampling from each galaxy's P(z) can give wrong
answers (because this magnifies photo-z spread rather than
compensating for it). Exploiting the LSST dataset will require
supporting research into methods for inference using photo-zs and
supporting the community in developing and releasing publicly
available code and tools.