We propose and illustrate a hierarchical Bayesian approach for matching
statistical records observed on different occasions. We show how this model can
be profitably adopted both in record linkage problems and in capture--recapture
setups, where the size of a finite population is the real object of interest.
There are at least two important differences between the proposed model-based
approach and the current practice in record linkage. First, the statistical
model is built up on the actually observed categorical variables and no
reduction (to 0--1 comparisons) of the available information takes place.
Second, the hierarchical structure of the model allows a two-way propagation of
the uncertainty between the parameter estimation step and the matching
procedure so that no plug-in estimates are used and the correct uncertainty is
accounted for both in estimating the population size and in performing the
record linkage. We illustrate and motivate our proposal through a real data
example and simulations.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS447 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
