On the use of Bayesian Monte-Carlo in evaluation of nuclear data
On the use of Bayesian Monte-Carlo in evaluation of nuclear data
复制标题
贝叶斯蒙特卡罗在核数据评估中的应用
DOI：
10.1051/epjconf/201714602007
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
G. Noguere
中科院分区：
文献类型：
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作者：
C. D. S. Jean;P. Archier;E. Privas;G. Noguere
作为模型参数，理论模型的必要成分，并不总是预测的理论，一个正式的数学框架相关联的评估工作，需要获得最佳的一组参数（共振参数，光学模型，裂变势垒，平均宽度，多群截面）与贝叶斯统计推断，通过比较理论与实验。与这种方法相关的正式规则是通过求解以下类型的方程来估计一组参数的后验密度概率函数：pdf（后验）× pdf（先验）×似然函数。拟合过程可以被看作是已知关于这些参数的先验信息的一组参数（称为x→）的后验密度概率的估计，以及给出观测已知x→的数据集的概率密度函数的似然。为了解决这个问题，可以采取两种主要途径：添加近似和假设，并获得要数值求解的方程（成本函数的最小值或广义最小二乘法，简称GLS）或使用所有先验分布的蒙特-卡罗采样，并估计最终的后验分布。蒙特卡罗方法是贝叶斯推理问题的自然解决方案。他们避免了近似（存在于基于卡方最小化的传统调整过程中），并在先验和似然的概率密度分布的选择中提出了替代方案。本文将提出使用我们所谓的贝叶斯蒙特卡罗（简称BMC在其余的手稿）在整个能量范围内，从热，共振和连续范围的所有核反应模型在这些能量。算法将基于蒙特-卡罗采样和马尔可夫链。BMC的目标是提出一个参考计算，以验证GLS计算和近似，测试概率密度分布的影响，并提供框架，找到全球最小值，如果存在几个局部最小值。应用解决共振，未解决的共振和连续评价以及多组截面数据同化。
As model parameters, necessary ingredients of theoretical models, are not always predicted by theory, a formal mathematical framework associated to the evaluation work is needed to obtain the best set of parameters (resonance parameters, optical models, fission barrier, average width, multigroup cross sections) with Bayesian statistical inference by comparing theory to experiment. The formal rule related to this methodology is to estimate the posterior density probability function of a set of parameters by solving an equation of the following type: pdf(posterior) ∼ pdf(prior) × a likelihood function. A fitting procedure can be seen as an estimation of the posterior density probability of a set of parameters (referred as x→ ) knowing a prior information on these parameters and a likelihood which gives the probability density function of observing a data set knowing x→ . To solve this problem, two major paths could be taken: add approximations and hypothesis and obtain an equation to be solved numerically (minimum of a cost function or Generalized least Square method, referred as GLS) or use Monte-Carlo sampling of all prior distributions and estimate the final posterior distribution. Monte Carlo methods are natural solution for Bayesian inference problems. They avoid approximations (existing in traditional adjustment procedure based on chi-square minimization) and propose alternative in the choice of probability density distribution for priors and likelihoods. This paper will propose the use of what we are calling Bayesian Monte Carlo (referred as BMC in the rest of the manuscript) in the whole energy range from thermal, resonance and continuum range for all nuclear reaction models at these energies. Algorithms will be presented based on Monte-Carlo sampling and Markov chain. The objectives of BMC are to propose a reference calculation for validating the GLS calculations and approximations, to test probability density distributions effects and to provide the framework of finding global minimum if several local minimums exist. Application to resolved resonance, unresolved resonance and continuum evaluation as well as multigroup cross section data assimilation will be presented.