The EEPAS Model Revisited: Statistical Formalism and a High-Performance, Reproducible Open-Source Framework

While short-term models such as the Short-Term Earthquake Probability (STEP) and Epidemic-Type Aftershock Sequence (ETAS) are well established and supported by open-source software, medium- to long-term models, notably the Every Earthquake a Precursor According to Scale (EEPAS) and Proximity to Past Earthquakes (PPE), remain under-documented and largely inaccessible. Despite outperforming time-invariant models in regional studies, their mathematical foundations are often insufficiently formalized. This study addresses these gaps by formally deriving the EEPAS and PPE models within the framework of inhomogeneous Poisson point processes and clarifying the connection between empirical $Ψ$-scaling regressions and likelihood-based inference. We introduce a fully automated, open-source Python implementation of EEPAS that combines analytical modeling with Numba JIT acceleration, NumPy vectorization, and joblib parallelization, all configured via modular JSON files for usability and reproducibility. Integration with pyCSEP enables standardized evaluation and comparison. When applied to the Italy HORUS dataset, our system reproduces published results within one hour using identical initialization settings. It also provides a comprehensive pipeline from raw catalog to parameter estimation, achieving improved log-likelihoods and passing strict consistency tests without manual $Ψ$ identification. We position our framework as part of a growing open-source ecosystem for seismological research that spans the full workflow from data acquisition to forecast evaluation. Our framework fills a key gap in this ecosystem by providing robust tools for medium- to long-term statistical modeling of earthquake catalogs, which is an essential but underserved component in probabilistic seismic forecasting.