Uncertainty decomposition method and its application in the liquid drop model

A method is suggested to decompose the statistical and systematic uncertainties from the total uncertainty of a theoretical model. The total uncertainty and the parameters of the model can be obtained through standard statistical fitting procedures. Present work concentrates on the decomposition of the total uncertainty after fitting procedure. The distribution of the total uncertainty is considered as two normal distributions, corresponding to statistical and systematic uncertainties, respectively. The standard deviation of the statistical part, $\sigma_{stat}$, is estimated through random parameters distributed around their best fitted values. The two normal distributions are obtained by minimizing the moments of the total uncertainty with fixed $\sigma_{stat}$. The method is applied to the liquid drop model (LDM). The statistical and systematic uncertainties are decomposed from the total uncertainty of the nuclear binding energies with and without the consideration of the shell effect in LDM. The estimated distributions of the statistical and systematic uncertainties can well describe that of the total uncertainty.