QENS数据的贝叶斯分析：从参数确定到模型选择
Bayesian Analysis of QENS data: From parameter determination to model selection
摘要：
从准弹性中子散射谱中提取任何物理信息，一般都是通过卡方最小化方法对数据进行模型拟合来完成的。然而，正如D. S. Sivia等人，也可以采用基于贝叶斯定理的另一概率方法。简而言之，经典卡方最小化和贝叶斯方法之间的主要区别是表达最终结果的方式：在第一种情况下，结果是一组具有对称误差和品质因数（如卡方）的参数值，而在第二种情况下，结果以参数和品质因数的概率分布函数（PDF）表示。在这方面的贡献，我们展示了如何最终PDF是通过探索所有可能的参数组合，与实验误差兼容。这种方法的三个优点将被强调：第一，参数之间的相关性被自动考虑，这意味着，例如，参数误差被正确计算，相关性以自然的方式出现，并且从它们的PDF中立即识别出不好定义的参数。第二，可以计算确定的物理模型的可能性，并且因此以正确定义的概率方式从许多模型中选择最适合具有最少数量的参数的数据的模型。
英文摘要：
The extraction of any physical information from quasielastic neutron scattering spectra is generally done by fitting a model to the data by means of chi-square minimization procedure. However, as pointed out by the pioneering work of D.S. Sivia et al., also another probabilistic approach based on Bayes theorem can be employed. In a nutshell, the main difference between the classical chi-square minimization and the Bayesian approach is the way of expressing the final results: In the first case, the result is a set of values of parameters with a symmetric error and a figure of merit such as chi-square, whereas in the second case the results are presented as probability distribution functions (PDF) of both, parameters and merit figure. In this contribution, we demonstrate how final PDFs are obtained by exploring all possible combinations of parameters that are compatible with the experimental error. Three advantages of this method will be emphasized: First, correlations between parameters are automatically taken into account, which implies, for example, that parameter errors are correctly calculated, correlations show up in a natural way and ill defined parameters are immediately recognized from their PDF. Second, it is possible to calculate the likelihood of a determined physical model, and therefore to select the one among many that fits the data best with a minimal number of parameters, in a correctly defined probabilistic way.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
