The Annals of Applied Statistics

A hierarchical Bayesian approach to record linkage and population size problems

Andrea Tancredi and Brunero Liseo

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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.

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Ann. Appl. Stat., Volume 5, Number 2B (2011), 1553-1585.

First available in Project Euclid: 13 July 2011

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Capture–recapture methods conditional independence Gibbs sampling Metropolis–Hastings record linkage


Tancredi, Andrea; Liseo, Brunero. A hierarchical Bayesian approach to record linkage and population size problems. Ann. Appl. Stat. 5 (2011), no. 2B, 1553--1585. doi:10.1214/10-AOAS447.

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Supplemental materials

  • Supplementary material: Data files and codes. Included in the supplementary material there are the following files: exampleA.dat, exampleB.dat and exampleV.dat contain the data used in Section 5. The files B.Cat.matching.example.R, example.R, functions.r, gibbs.c contain the codes. The file supplementary_figure.pdf shows the trace plots for the application described in Section 5.