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Abstract:
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Capture-recapture (CRC) surveys are widely used to estimate the size of a population whose members cannot be enumerated directly. When K capture samples are obtained, counts of unit captures in subsets of samples are represented naturally by a 2^K contingency table in which one element -- the number of individuals appearing in none of the samples -- remains unobserved. In the absence of additional assumptions, the population size is not point-identified. Independence assumptions are often used to achieve point-identification. However, real-world CRC surveys often use observational samples in which independence cannot be guaranteed. In this work, we apply the theory of partial identification to show that weak assumptions about the nature of dependence between samples can be used to characterize an identification region for the population size, such as the bounds on pairwise capture probabilities, and bounds on the highest order interaction term in the log-linear model. Estimators and confidence regions for the identification region are derived for each scenario. We apply these methods to recent survey data to estimate the number of people who inject drugs in Brussels, Belgium.
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