Frequentist and Bayesian inference for interacting point process models of recurrent events

The modeling of interacting point processes provides a flexible framework for studying systems where events in one process influence the rate of future events of another. In this work, we investigate two-way interaction models in which excitatory or inhibitory effects operate within fixed carryover windows. Such mechanisms capture clustering or suppression of recurrent events and are relevant in diverse applications, ranging from finance to cybersecurity. We examine the estimation of these interaction effects under both frequentist and Bayesian paradigms. We develop simulation procedures for likelihood-based estimation and implement Bayesian inference through Metropolis sampling. We illustrate the methodology with financially inspired synthetic dataset. Finally, we propose future directions involving model assessments and extensions to more complex interaction processes.