  In database management, record linkage aims to identify multiple records that
correspond to the same individual. This task can be treated as a clustering
problem, in which a latent entity is associated with one or more noisy database
records. However, in contrast to traditional clustering applications, a large
number of clusters with a few observations per cluster is expected in this
context. In this paper, we introduce a new class of prior distributions based
on allelic partitions that is specially suited for the small cluster setting of
record linkage. Our approach makes it straightforward to introduce prior
information about the cluster size distribution at different scales, and
naturally enforces sublinear growth of the maximum cluster size -known as the
microclustering property. We also introduce a set of novel microclustering
conditions in order to impose further constraints on the cluster sizes a
priori. We evaluate the performance of our proposed class of priors using
simulated data and three official statistics data sets, and show that our
models provide competitive results compared to state-of-the-art microclustering
models in the record linkage literature. Moreover, we compare the performance
of different loss functions for optimal point estimation of the partitions
using decision-theoretical based approaches recently proposed in the
literature.
