  We introduce a new method to estimate the probability that an extragalactic
transient source is associated with a candidate host galaxy. This approach
relies solely on simple observables: sky coordinates and their uncertainties,
galaxy fluxes and angular sizes. The formalism invokes Bayes' rule to calculate
the posterior probability P(O_i|x) from the galaxy prior P(O), observables x,
and an assumed model for the true distribution of transients in/around their
host galaxies. Using simulated transients placed in the well-studied COSMOS
field, we consider several agnostic and physically motivated priors and offset
distributions to explore the method sensitivity. We then apply the methodology
to the set of 13~fast radio bursts (FRBs) localized with an uncertainty of
several arcseconds. Our methodology finds nine of these are securely associated
to a single host galaxy, P(O_i|x)>0.95. We examine the observed and intrinsic
properties of these secure FRB hosts, recovering similar distributions as
previous works. Furthermore, we find a strong correlation between the apparent
magnitude of the securely identified host galaxies and the estimated cosmic
dispersion measures of the corresponding FRBs, which results from the Macquart
relation. Future work with FRBs will leverage this relation and other measures
from the secure hosts as priors for future associations. The methodology is
generic to transient type, localization error, and image quality. We encourage
its application to other transients where host galaxy associations are critical
to the science, e.g. gravitational wave events, gamma-ray bursts, and
supernovae. We have encoded the technique in Python on GitHub:
https://github.com/FRBs/astropath.
