Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions

Abstract

Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with the elastic and the transfer process for both methods, which are evaluated against data via a comparison of the empirical coverage probabilities. Expectedly, the frequentist approach is not as flexible as the Bayesian approach in exploring parameter space and often ends up in a different minimum. We also show that the two methods produce significantly different correlations. In the end, the frequentist approach produces significantly narrower uncertainties on the considered observables than the Bayesian. Our study demonstrates that the uncertainties on the reaction observables considered here within the Bayesian approach represent reality more accurately than the much narrower uncertainties obtained using the standard frequentist approach.

Elastic transfer and parity dependence of the nucleus-nucleus optical potential

“…Beginning with standard covariance propagation methods [26,28] and moving on to Bayesian methods [27], we have quantified uncertainties from the fitting of optical potentials to nucleon elastic scattering and then propagated them to transfer cross sections, using both the distorted wave Born approximation (DWBA) and the adiabatic wave approximation (ADWA). We have also made a direct and systematic comparison between the frequentist χ 2 optimization and Bayesian methods [29]. This study showed that, despite popular belief, the two methods are not identical and that, for the higher levels of confidence, frequentist methods severely underestimate the uncertainties while the Bayesian approach provides a truer representation of the uncertainty.…”

“…The present work comes in the sequence of a number of uncertainty quantification (UQ) studies [25][26][27][28][29]: The goal is to use modern statistical tools to reliably understand, quantify, and control uncertainties in the theory for direct reactions. Over the past few years, our UQ efforts have focused on the parametric uncertainties associated with the nucleon-target optical potential, when informed by elastic scattering, and understanding how those uncertainties propagate to deuteroninduced transfer reactions.…”

“…The goal of the present work is to explore different avenues to reduce the uncertainties found in Refs. [26][27][28][29]. The UQ methods we begin to explore here fall under the umbrella of Bayesian experimental design [34] and should be applicable across the nuclear chart, whenever the concept of an optical potential holds.…”

Mean Shift Cluster Recognition Method Implementation in the Nested Sampling Algorithm

“…At present, Bayesian methods are routinely used in many fields: astrophysics and cosmology [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ], particle physics [ 9 ], plasma physics [ 10 , 11 ], machine learning [ 12 ] and many others [ 13 , 14 ]. In the past few years, they were also applied to nuclear [ 15 , 16 ] and atomic physics [ 17 , 18 , 19 , 20 , 21 ]. On one hand, one of the reasons for this success is related to the possibility of assigning a probability value to models (hypotheses) from the analysis of the same set of data in a very defined framework.…”

Biophysically Informed Imaging Acquisition of Plant Water Status

“…Hierarchical Bayesian approaches provide robust, testable predictions from the data in hand while allowing for probabilistic testing of false positives interacting with model complexity and probabilistic exploration of measurement error (Olejnik and Algina, 1983;Press, 2005;Lu et al, 2017). Both of these benefits are crucial when using different types of measurements to increase transparency in the analyses and inferences using explicit priors and credible intervals to better explain the variation in the data (Samanta et al, 2007;Ogle and Barber, 2008;Quaife and Cripps, 2016;King et al, 2019;Phillipson et al, 2020).…”