  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. Approaches to
multiple-systems estimation often do not emphasize the role of the identifying
assumption during model specification, which makes it difficult to decouple the
specification of the model for the observed data from the identifying
assumption. We present a re-framing of the multiple-systems estimation problem
that decouples the specification of the observed-data model from the
identifying assumptions, and discuss how log-linear models and the associated
no-highest-order interaction assumption fit into this framing. We present an
approach to computation in the Bayesian setting which takes advantage of
existing software and facilitates various sensitivity analyses. We demonstrate
our approach in a case study of estimating the number of civilian casualties in
the Kosovo war. Code used to produce this manuscript is available at
https://github.com/aleshing/revisiting-identifying-assumptions.
