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The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data. If an appropriate identifying assumption cannot be found for a data set, no estimate of the population size should be produced based on that data set, as models with different identifying assumptions can produce arbitrarily different population size estimates—even with identical observed data fits. Approaches to multiple-systems estimation often do not explicitly specify identifying assumptions. This makes it difficult to decouple the specification of the model for the observed data from the identifying assumption and to provide justification for the identifying assumption. We present a re-framing of the multiple-systems estimation problem that leads to an approach which decouples the specification of the observed-data model from the identifying assumption, and discuss how common models fit into this framing. This approach takes advantage of existing software and facilitates various sensitivity analyses. We demonstrate our approach in a case study estimating the number of civilian casualties in the Kosovo war. Code used to produce this manuscript is available at github.com/aleshing/central-role-of-identifying-assumptions 

Merging datafiles containing information on overlapping sets of entities is a challenging task in the absence of unique identifiers, and is further complicated when some entities are duplicated in the datafiles. Most approaches to this problem have focused on linking two files assumed to be free of duplicates, or on detecting which records in a single file are duplicates. However, it is common in practice to encounter scenarios that fit somewhere in between or beyond these two settings. We propose a Bayesian approach for the general setting of multifile record linkage and duplicate detection. We use a novel partition representation to propose a structured prior for partitions that can incorporate prior information about the data collection processes of the datafiles in a flexible manner, and extend previous models for comparison data to accommodate the multifile setting. We also introduce a family of loss functions to derive Bayes estimates of partitions that allow uncertain portions of the partitions to be left unresolved. The performance of our proposed methodology is explored through extensive simulations. Supplementary materials for this article are available online.