Bayesian Gaussian Methods for Robust Background Modeling in CALorimetric Electron Telescope (CALET) Gravitational-Wave Searches

The search for gamma-ray counterparts to gravitational-wave events with the CALET Gamma-ray Burst Monitor (CGBM) requires accurate and robust background modeling. Previous CALET observing runs (O3 and O4) relied on averaged pre/post-event baselines or low-order polynomial fits, approaches that neglect correlated noise, temporal non-stationarity, and the propagation of background uncertainty into derived flux upper limits. These simplifications can lead to reduced sensitivity to faint or atypical transients. In this work, we present a novel Bayesian framework for background estimation based on Gaussian Process (GP) regression and change-point modeling. Our approach captures correlated structures in the detector background, quantifies predictive uncertainties, and propagates them into both detection statistics and Bayesian credible upper limits. We demonstrate, using archival CALET time-tagged event data and simulated signal injections, that our method improves sensitivity to weak short-duration bursts by up to an order of magnitude compared to traditional polynomial fits. This probabilistic background treatment enables a more physically robust interpretation of non-detections and offers a scalable, real-time compatible extension for future joint multi-messenger searches. All codes used in this paper are available at https://github.com/SMALLSCALEDEV/Bayesian-Gaussian-Approach-for-Background-Estimation-in-CALET-GW.