A Bayesian Inference Framework for Binary Lens Events Fully Incorporating Higher-Order Effects

Higher-order effects, such as microlensing parallax and lens orbital motion, are essential for characterizing the physical properties of microlensing planetary systems including their masses and distances. In practice, higher-order effects are often included in light-curve modeling only when their signals are strong, because their inclusion in weakly constrained cases tends to drive the inferred parameters toward regions of parameter space that are disfavored by standard Galactic models. This binary choice over physically continuous effects introduces an event-dependent selection function that complicates population-level interpretation and prevents strong and weak detections from being combined within a single uniform framework. In this work, we investigate the origin of instabilities associated with higher-order effects, and show that such instabilities can arise from a mismatch between commonly adopted uninformative priors in the light-curve parameter space and the distributions predicted by Galactic models. Motivated by this, we develop a new Bayesian framework that enables higher-order effects to be incorporated in a stable and uniform manner. As part of this framework, we introduce Galactic Prior Modeling Engine (gapmoe), a dedicated tool that enables efficient evaluation of the Galactic prior density and allows it to be incorporated directly into the light-curve inference. Using simulated events, we demonstrate that our framework robustly recovers the true physical parameters while fully accounting for microlensing parallax and lens orbital motion. This framework eliminates the need for ad-hoc model selection and provides a scalable and statistically consistent pathway for analyzing the large samples expected from next-generation surveys such as the Roman Space Telescope.