Multiple Systems Estimation (or Capture-Recapture Estimation) to Inform Public Policy.

Estimating population sizes has long been of interest, from the estimation of the human or ecological population size within regions or countries to the hidden number of civilian casualties in a war. Total enumeration of the population, for example, via a census, is often infeasible or simply impractical. However, a series of partial enumerations or observations of the population is often possible. This has led to the ideas of capture-recapture methods, which have been extensively used within 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 the multiple lists. This is often referred to as Multiple Systems Estimation (MSE). The MSE approach has been preferred when estimating "capture-shy" or hard-to-reach populations, including those caught up in the criminal justice system; or homeless; or trafficked; or civilian casualties of war. Motivated by a range of public policy applications of MSE, each briefly introduced, we discuss practical problems with potentially substantial methodological implications. They include: "period" definition; "case" definition; 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 different lists; demographic or other information about the "case" which may influence capture-propensities; required permissions to access extant-lists; list-creation by research-teams or interested parties; referrals (if presence on list A results - almost surely - in presence on list B); 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 on whether the uncertainty which qualified their estimates was sufficiently narrow to orient public policy; and, if not, what options were available and/or taken to reduce the uncertainty or to seek external validation. We also consider whether MSE was hypothesis-generating: in the sense of having spawned new lines of inquiry.