考虑认知不确定性的模型确认贝叶斯因子法

Bayes factor for model validation under epistemic uncertainty

针对认知不确定性条件下计算机建模仿真所面临的模型确认问题,提出一种结合了二阶概率法与区间数排序的改进贝叶斯模型确认方法。该方法首先采用二阶概率法对模型的不确定性进行量化,量化结果被作为先验模型输出,再基于实验数据对模型输出的先验概率密度进行贝叶斯更新,最后通过区间数排序的方式对比模型输出的后验和先验概率密度。由此所得的贝叶斯因子能够在模型存在认知不确定性的情况下为模型确认提供可信的结果。算例分析结果显示了该方法的合理性。

Considering computer model validation under epistemic uncertainty, this paper developed an improved Bayesian model validation method which combined the second order probability method and the interval number rank method. The meth- od first accomplished the model uncertainty quantification by the second order probability method. Then it updated the prior model response computed from uncertainty quantification based on experimental observation using Bayesian theory. Finally it used the method for ranking interval numbers to contrast the posterior probability density of the model response with the prior probability density. The obtained Bayes factor provided a credible result for model validation under epistemic uncertainty. Simu- lation results show that the ~resented method is rational.