Bayesian probability updates using Sampling/Importance Resampling: Applications in nuclear theory

TL;DR

This paper reviews the sampling/importance resampling method within Bayesian inference, illustrating its applications and limitations in nuclear theory, particularly for parameter estimation and observable prediction.

Contribution

It provides a detailed analysis of importance resampling's usefulness in nuclear physics and demonstrates its application to chiral effective field theory models.

Findings

Effective in estimating posterior distributions for nuclear interaction parameters.

Demonstrates realistic applications in nuclear physics modeling.

Shows limitations of importance resampling in extreme cases.

Abstract

We review an established Bayesian sampling method called sampling/importance resampling and highlight situations in nuclear theory when it can be particularly useful. To this end we both analyse a toy problem and demonstrate realistic applications of importance resampling to infer the posterior distribution for parameters of $\Delta$NNLO interaction model based on chiral effective field theory and to estimate the posterior probability distribution of target observables. The limitation of the method is also showcased in extreme situations where importance resampling breaks.