From Fractions to Individuals: Information-Theoretic Integerization for Population Synthesis

Abstract

Every population synthesis method produces fractional expected counts, but simulation models require whole individuals. This paper treats integerization as an inference problem: among all feasible integer tables, choose the one closest to the fractional baseline in Kullback–Leibler divergence. We show that an optimal solution always assigns each cell either its floor or ceiling value, which reduces the task to a deterministic two-step procedure: a second IPF pass on the residuals followed by largest-remainder allocation. Applied to 98 Danish municipalities with 635,000 joint cells, the method places 98.4% of population mass in the correct cells compared with 92.1% for multinomial sampling, while preserving controlling margins exactly and eliminating run-to-run sampling noise.