  We propose the use of robust, Bayesian methods for estimating extragalactic
distance errors in multi-measurement catalogs. We seek to improve upon the more
commonly used frequentist propagation-of-error methods, as they fail to explain
both the scatter between different measurements and the effects of skewness in
the metric distance probability distribution. For individual galaxies, the most
transparent way to assess the variance of redshift independent distances is to
directly sample the posterior probability distribution obtained from the
mixture of reported measurements. However, sampling the posterior can be
cumbersome for catalog-wide precision cosmology applications. We compare the
performance of frequentist methods versus our proposed measures for estimating
the true variance of the metric distance probability distribution. We provide
pre-computed distance error data tables for galaxies in 3 catalogs: NED-D,
HyperLEDA, and Cosmicflows-3. Additionally, we develop a Bayesian model that
considers systematic and random effects in the estimation of errors for
Tully-Fisher relation (TF) derived distances in NED-D. We validate this model
with a Bayesian $p$-value computed using the Freeman-Tukey discrepancy measure
as a posterior predictive check. We are then able to predict distance errors
for 884 galaxies in the NED-D catalog and 203 galaxies in the HyperLEDA catalog
which do not report TF distance modulus errors. Our goal is that our estimated
and predicted errors are used in catalog-wide applications that require
acknowledging the true variance of extragalactic distance measurements.

Instrumentation and Methods for Astrophysics;Astrophysics of Galaxies