  Probabilistic record linkage (PRL) is the process of determining which
records in two databases correspond to the same underlying entity in the
absence of a unique identifier. Bayesian solutions to this problem provide a
powerful mechanism for propagating uncertainty due to uncertain links between
records (via the posterior distribution). However, computational considerations
severely limit the practical applicability of existing Bayesian approaches. We
propose a new computational approach, providing both a fast algorithm for
deriving point estimates of the linkage structure that properly account for
one-to-one matching and a restricted MCMC algorithm that samples from an
approximate posterior distribution. Our advances make it possible to perform
Bayesian PRL for larger problems, and to assess the sensitivity of results to
varying prior specifications. We demonstrate the methods on simulated data and
an application to a post-enumeration survey for coverage estimation in the
Italian census.
