In nuclear density functional theory (DFT), uncertainties in theoretical predictions can be categorized into two types: statistical errors originating from intra-model parameter uncertainties and systematic errors arising from inter-model discrepancies. The former results from the propagation of experimental uncertainties during parameter calibration, whereas the latter reflects systematic deviations in predicting the same physical quantity across different models.

This study aims to review the application of Bayesian uncertainty quantification in nuclear DFT, addressing both intra- and inter-model uncertainties.

The Bayesian inference approach was first introduced. Subsequently, two representative applications in DFT uncertainty quantification were presented: 1) Bayesian parameter estimation utilizing machine learning techniques to quantify parameter uncertainties within the nonlinear relativistic mean field (RMF) model; 2) Bayesian model averaging to analyze systematic uncertainties in symmetry energy at 2/3 saturation density between Skyrme energy density functionals and RMF models.

The Bayesian parameter estimation method effectively quantifies statistical intra-model uncertainties, while Bayesian model averaging offers a robust statistical framework for quantifying inter-model uncertainties, enhancing the reliability of nuclear property predictions.

The application of Bayesian inference in both parameter estimation and model averaging provides valuable tools for addressing uncertainties in nuclear physics.