  We present a Bayesian approach to the redshift classification of
emission-line galaxies when only a single emission line is detected
spectroscopically. We consider the case of surveys for high-redshift
Lyman-alpha-emitting galaxies (LAEs), which have traditionally been classified
via an inferred rest-frame equivalent width (EW) greater than 20 angstrom. Our
Bayesian method relies on known prior probabilities in measured emission-line
luminosity functions and equivalent width distributions for the galaxy
populations, and returns the probability that an object in question is an LAE
given the characteristics observed. This approach will be directly relevant for
the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), which seeks to
classify ~10^6 emission-line galaxies into LAEs and low-redshift [O II]
emitters. For a simulated HETDEX catalog with realistic measurement noise, our
Bayesian method recovers 86% of LAEs missed by the traditional EW > 20 angstrom
cutoff over 2 < z < 3, outperforming the EW cut in both contamination and
incompleteness. This is due to the method's ability to trade off between the
two types of binary classification error by adjusting the stringency of the
probability requirement for classifying an observed object as an LAE. In our
simulations of HETDEX, this method reduces the uncertainty in cosmological
distance measurements by 14% with respect to the EW cut, equivalent to
recovering 29% more cosmological information. Rather than using binary object
labels, this method enables the use of classification probabilities in
large-scale structure analyses. It can be applied to narrowband emission-line
surveys as well as upcoming large spectroscopic surveys including Euclid and
WFIRST.

Instrumentation and Methods for Astrophysics;Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies