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Continuous time‐interaction processes for population size estimation, with an application to drug dealing in Italy

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  • Linda Altieri
  • Alessio Farcomeni
  • Danilo Alunni Fegatelli

Abstract

We introduce a 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 timescales; other effects such as those of 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 about the estimation of the total number of drug dealers in Italy. To do so, we derive a conditional likelihood formulation where only subjects with at least one capture are involved in the inference process. The result is a novel and flexible continuous‐time population size estimator. A simulation study and the analysis of our motivating example illustrate the validity of our approach in several scenarios.

Suggested Citation

  • Linda Altieri & Alessio Farcomeni & Danilo Alunni Fegatelli, 2023. "Continuous time‐interaction processes for population size estimation, with an application to drug dealing in Italy," Biometrics, The International Biometric Society, vol. 79(2), pages 1254-1267, June.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:1254-1267
    DOI: 10.1111/biom.13662
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    References listed on IDEAS

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