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Bayesian neural network (BNN) approach is employed to improve the predictions of nuclear masses and half-lives. It is found that the noise error in the likelihood function plays an important role in the predictive performance for the BNN approach. By including a distribution for the noise error, theoretical predictions can be improved remarkably. In addition to the proton and mass numbers, we further include two quantities related to nuclear pairing and shell effects into the input layer for nuclear mass predictions, and two quantities related to nuclear pairing and reaction energies into the input layer for nuclear half-life predictions. As a result, the theoretical accuracies are significantly improved for both nuclear masses and nuclear half-lives. This manifests that better predictive performance can be achieved if more physical features are included into the BNN approach.