Applications of estimating population sizes range from estimating human or ecological population size within regions or countries to estimating the hidden number of civilian casualties in war. Total enumeration via a census is typically infeasible. However, a series of partial enumerations of a population is often possible, leading to capture-recapture methods, which have been extensively used in ecology to estimate the size of wildlife populations with an associated measure of uncertainty and are most effectively applied when there are multiple capture occasions. Capture-recapture ideology can be more widely applied to multiple data sources by the linkage of individuals across multiple lists, often referred to as multiple systems estimation (MSE). The MSE approach is preferred when estimating capture-shy or hard-to-reach populations, including those who are caught up in the criminal justice system, trafficked, or civilian casualties of war. Motivated by the public policy applications of MSE, each briefly introduced, we discuss practical problems with methodological implications. They include period definition; case definition; scenarios when an observed count is not a true count of the population of interest but an upper bound due to mismatched definitions; exact or probabilistic matching of cases across lists; demographic or other information about the case that influences capture propensities; permissions to access lists; list creation by research teams or interested parties; referrals (if presence on list results, almost surely, in presence on list ); different mathematical models leading to widely different estimated population sizes; uncertainty in estimation; computational efficiency; external validation; hypothesis generation; and additional independent external information. Returning to our motivational applications, we focus finally on whether the uncertainty that qualified their estimates was sufficiently narrow to orient public policy.


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