核反应的贝叶斯和频率论不确定性量化的直接比较
Direct comparison between Bayesian and frequentist uncertainty quantification for nuclear reactions
摘要：
直到最近，低能核理论中的不确定性量化通常使用频率论方法进行。然而，在过去的几年里，该领域已经转向贝叶斯统计评估置信区间。虽然有统计学上的论点倾向于贝叶斯方法，但没有直接的比较。在这项工作中，我们比较，直接和系统地，频率论和贝叶斯方法来量化直接核反应的不确定性。从相同的初始假设开始，我们确定了与弹性和转移过程相关的置信区间，这两种方法，通过比较经验覆盖概率对数据进行评估。可以预期的是，频率论方法在探索参数空间方面不如贝叶斯方法灵活，并且通常会以不同的最小值结束。我们还表明，这两种方法产生显着不同的相关性。最后，频率论的方法产生显着更窄的不确定性所考虑的观测比贝叶斯。我们的研究表明，反应的不确定性在这里考虑贝叶斯方法更准确地代表现实比窄得多的不确定性使用标准的频率论方法。
英文摘要：
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.
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