Continuous Time-Interaction Processes for Population Size Estimation, with an Application to Drug Dealing in Italy

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.

Finite mixtures in capture–recapture surveys for modeling residency patterns in marine wildlife populations

“…Original applications of such methods date back to the beginning of the 20th century and were based on standard homogeneity assumptions on the population structure and the identification process (Amstrup et al., 2010; Le Cren, 1965). The literature is now rich in alternatives that can address a large variety of deviations from such basic model assumptions and suit situations where, for example, individuals exhibit heterogeneous behaviors (Pledger, 2000), sampling occurs in continuous time (Altieri et al., 2023), stop‐over sites are present (Matechou et al., 2013; Worthington et al., 2019; Wu et al., 2021), temporary emigration is allowed (Zhou et al., 2019), and so on. For an exhaustive review, see King and McCrea (2019) and references therein.…”

Approximation of Bayesian Hawkes process with inlabru

“…Hawkes processes or self-exciting processes, first introduced by Hawkes (1971aHawkes ( , 1971b, are counting processes often used to model the "arrivals" of some events over time, when each arrival increases the probability of subsequent arrivals in its proximity. Typical applications can be found in seismology (Ogata, 1988(Ogata, , 2011Ogata & Zhuang, 2006;Schoenberg, 2022), capture-recapture (Altieri et al, 2022;Weller et al, 2018), invasive species (Balderama et al, 2012), droughts (Li et al, 2021), crime (Mohler, 2013;Mohler et al, 2011Mohler et al, , 2018, finance (Azizpour et al, 2018;Filimonov & Sornette, 2012;Hawkes, 2018), disease mapping (Chiang et al, 2022;Garetto et al, 2021), wildfires (Peng et al, 2005), and social network analysis (Kobayashi & Lambiotte, 2016;Zhou et al, 2013).…”