The bipartite record linkage task consists of merging two disparate datafiles containing
information on two overlapping sets of entities. This is non-trivial in the absence
of unique identifiers and it is important for a wide variety of applications given
that it needs to be solved whenever we have to combine information from different
sources. Most statistical techniques currently used for record linkage are derived from
a seminal paper by Fellegi and Sunter (1969). These techniques usually assume independence
in the matching statuses of record pairs to derive estimation procedures
and optimal point estimators. We argue that this independence assumption is unreasonable
and instead target a bipartite matching between the two datafiles as our
parameter of interest. Bayesian implementations allow us to quantify uncertainty on
the matching decisions and derive a variety of point estimators using different loss
functions. We propose partial Bayes estimates that allow uncertain parts of the bipartite
matching to be left unresolved. We evaluate our approach to record linkage
using a variety of challenging scenarios and show that it outperforms the traditional
methodology. We illustrate the advantages of our methods merging two datafiles on
casualties from the civil war of El Salvador.