  Probabilistic record linkage, the task of merging two or more databases in
the absence of a unique identifier, is a perennial and challenging problem. It
is closely related to the problem of deduplicating a single database, which can
be cast as linking a single database against itself. In both cases the number
of possible links grows rapidly in the size of the databases under
consideration, and in most applications it is necessary to first reduce the
number of record pairs that will be compared.
  Spurred by practical considerations, a range of methods have been developed
for this task. These methods go under a variety of names, including indexing
and blocking, and have seen significant development. However, methods for
inferring linkage structure that account for indexing, blocking, and additional
filtering steps have not seen commensurate development. In this paper we review
the implications of indexing, blocking and filtering within the popular
Fellegi-Sunter framework, and propose a new model to account for particular
forms of indexing and filtering.
