Comparing Methods of Inferring Population Size from Incomplete Travel Data

Bryan Baker, U.S. Department of Homeland Security (DHS)

The U.S. Department of Homeland Security (DHS) uses observed arrival dates from administrative arrival records and expected departure dates from synthetic departure records to estimate the size of the resident nonimmigrant population (temporary, legal migrants) in the United States during a given period of time. The existing DHS method synthesizes departure dates by adding an estimate of the average visit length to the observed arrival dates, where the average visit length is estimated from completed visit records with a departure recorded in 2008. One alternative to the existing method would be to assign a probability to every possible visit length for every visit using the frequency distribution from the same set of completed visit records. This paper will compare the estimated population size using the existing method with estimates generated using the frequency distribution, a gamma time-until-failure distribution with parameters chosen to fit the frequency distribution, and an average of multiple hot-deck simulations.