Limited availability of recorded ground motions poses a challenge for reliable probabilistic seismic-hazard analysis (PSHA), even in highly seismic regions like the Western United States. Stochastic ground motions are commonly employed to address this challenge. However, the stochastic ground motion models (GMMs) may not consistently generate ground motions compatible with the site hazard due to their calibration using global data, failing to capture site-specific characteristics adequately. In the absence of recorded motions, physics-informed simulations provide a viable alternative but are deterministic with limitations of their own that makes them challenging to support PSHA. This article introduces a Bayesian framework that combines prior knowledge from a stochastic GMM, calibrated with global data, with site-specific data obtained from deterministic physics-informed simulations. The proposed framework utilizes the Rezaeian–Der Kiureghian (2010) model as the stochastic GMM and incorporates site-specific data from the CyberShake 15.12 study. By updating the mean and variance of the predictive relationships, along with the marginal distribution of the model parameters, through Bayesian inference, this framework allows for the simulation of site-specific ground motions consistent with the site characteristics. The statistics of peak ground acceleration distributions, as well as both the median and variability of the elastic response spectra, obtained from the calibrated stochastic GMM, demonstrate consistency with those derived using GMMs based on the Next Generation Attenuation (NGA) database.