Uncertainty decomposition method and its application in the liquid drop model

TL;DR

This paper introduces a method to decompose total uncertainty into statistical and systematic parts in nuclear models, applied specifically to the liquid drop model, improving understanding of model residues and uncertainties.

Contribution

A novel approach to separate statistical and systematic uncertainties from model residues, validated on the liquid drop model for nuclear binding energies.

Findings

Statistical and systematic uncertainties can be well described by normal distributions.

The method effectively decomposes uncertainties with and without shell effects.

Distributions align with physical expectations for different nuclei types.

Abstract

A method is suggested to decompose the statistical and systematic uncertainties from the residues between the calculation of a theoretical model and the observed data. The residues and the parameters of the model can be obtained through the standard statistical fitting procedures. The present work concentrates on the decomposition of the total uncertainty, of which the distribution corresponds to that of the residues. The distribution of the total uncertainty is considered as two normal distributions, statistical and systematic uncertainties. 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 distribution of the residues with the fixed {\sigma}stat. The method is applied to the liquid drop model (LD). The statistical and systematic uncertainties are decomposed from the residues of the nuclear binding energies with and without the consideration of the shell effect in LD. The estimated distributions of the statistical and systematic uncertainties can well describe that of the residues. The normal assumption of the distribution of the statistical and systematic uncertainties is examined through various approaches. The comparison between the distributions of the specific nuclei and those of the statistical and systematic uncertainties are consistent with the physical considerations, although the latter two can be obtained without the knowledge of these considerations. Such as, the LD are more suitable to describe the heavy nuclei. The light and heavy nuclei are indeed distributed mostly inside the distributions of the statistical and systematic uncertainties, respectively. The similar situation are also found for the nuclei close to and far from shell. The present method is also performed to nuclei around stability line.