  Gravitational waves emitted during compact binary coalescences are a
promising source for gravitational-wave detector networks. The accuracy with
which the location of the source on the sky can be inferred from gravitational
wave data is a limiting factor for several potential scientific goals of
gravitational-wave astronomy, including multi-messenger observations. Various
methods have been used to estimate the ability of a proposed network to
localize sources. Here we compare two techniques for predicting the uncertainty
of sky localization -- timing triangulation and the Fisher information matrix
approximations -- with Bayesian inference on the full, coherent data set. We
find that timing triangulation alone tends to over-estimate the uncertainty in
sky localization by a median factor of $4$ for a set of signals from
non-spinning compact object binaries ranging up to a total mass of $20
M_\odot$, and the over-estimation increases with the mass of the system. We
find that average predictions can be brought to better agreement by the
inclusion of phase consistency information in timing-triangulation techniques.
However, even after corrections, these techniques can yield significantly
different results to the full analysis on specific mock signals. Thus, while
the approximate techniques may be useful in providing rapid, large scale
estimates of network localization capability, the fully coherent Bayesian
analysis gives more robust results for individual signals, particularly in the
presence of detector noise.
