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

Area of Science:

• Statistics
• Epidemiology
• Computational Social Science

Background:

• Traditional point process models often struggle to capture complex event dynamics.
• Estimating population size, particularly in sensitive contexts like illicit activities, presents significant methodological challenges.
• Existing capture-recapture methods may not adequately account for temporal dependencies and event-triggered influences.

Purpose of the Study:

• To develop a novel time-interaction point process model incorporating self-excitement and self-correction mechanisms.
• To adapt the model for analyzing capture-recapture data, enabling flexible population size estimation.
• To address limitations in current statistical models by including covariates, unobserved heterogeneity, and temporal dependence.

Main Methods:

• Introduction of a continuous-time point process allowing events to influence future event probabilities (self-excitement/self-correction).
• Development of a conditional likelihood formulation tailored for capture-recapture data, focusing on observed individuals.
• Integration of covariates, unobserved heterogeneity, and temporal dependence within the point process framework.

Main Results:

• The proposed model provides a flexible and novel continuous-time population size estimator.
• A simulation study demonstrated the model's validity across various scenarios.
• Application to estimating the number of drug dealers in Italy showcased its practical utility.

Conclusions:

• The time-interaction point process offers a powerful new tool for analyzing complex event data.
• The derived conditional likelihood method effectively handles capture-recapture data for population estimation.
• This approach advances statistical modeling for ecological, epidemiological, and social science applications.