Continuous time-interaction processes for population size estimation, with an application to the number of drug dealers in Italy

Abstract: This work introduces a general time-interaction point process where the occurrence of an event can increase (self-excitement) or reduce (self-correction) the probability of future events. Self-excitement and self-correction are allowed to be triggered by the same event, at different time scales; other effects such as covariates, unobserved heterogeneity and temporal dependence are also allowed in the model. We focus on capture-recapture data, as our work is motivated by an original example where we need to estimate the total number of drug dealers in Italy. We derive a conditional likelihood formulation where only subjects with at least one observation are involved in the inference process, with the aim of obtaining continuous-time population size estimators. A simulation study illustrates the validity of our approach over a variety of scenarios, in comparison to a selection of the existing methods for population size estimation, as a support for the conclusions on our real data application.

Coautori: Alessio Farcomeni (b), Danilo Alunni-Fegatelli (c)

2. Faculty of Economics, University of Rome Tor Vergata
3.  Department of Public Health and Infectious Disease, University of Rome La Sapienza