Orthogonal Bayesian forecast combination for charge radii

Bayesian Model Combination (BMC) is an effective method to aid in scientific discoveries by combining the forecasts of imperfect theoretical models using Bayesian statistics and machine learning techniques. To mitigate the effect of model redundancy in the models' space, which can worsen predictive performance and uncertainty credible intervals, a pre-step of model orthogonalization via Principal Component Analysis (PCA) has been developed and successfully implemented in the case of nuclear binding energies (Giuliani P., Godbey K., et al, 2024). To explore extensions to various heterogenous datasets, in this current work, we apply and benchmark the developed PCA-BMC framework to nuclear charge radii. We find that missing physical effects in the models' space prevent the combined forecasts from yielding significant improvements over that of individual models. An analysis on 4 isotopic chain: Ca, Ni, Zn, Pb was conducted to support this result and future directions are explored to address this issue.