Plant-Capture Methods for Estimating Homeless Population Size From Uncertain Plant Captures

Plant-capture is a specialized variant of traditional capture-recapture methods used to estimate the size of a population. In epidemiologic literature, a notable application of this method is the estimation of the size of homeless populations through point-in-time street surveys. With this approach, decoys referred to as "plants" are introduced into the population to estimate the capture probability. Previous plant-capture studies have not systematically accounted for uncertainty in the capture status of individual plants. To address this, we propose three increasingly complex hierarchical modeling approaches to formally incorporate uncertainty into the plant-capture model arising from the capture status of plants and heterogeneity between survey sites. We then apply our methods to estimate the size of the homeless population in large US cities in the context of the "S-Night" study conducted by the US Census Bureau. Details on the frequentist and Bayesian implementations of our models, along with empirical evaluations of their statistical performance, are provided in the supplementary materials.