嵌套抽样算法用于地下水模型评价的算例研究

Application of nested sampling algorithm for assessing the uncertainty in groundwater flow model

模型评价(模型选择)是地下水数值模拟不确定分析的重要研究内容,模型边缘似然值是进行模型评价的重要依据。嵌套抽样算法是一种高效的高维积分计算方法,能有效计算复杂模型的边缘似然值。本次研究提出了一种基于Adaptive Metropolis的嵌套抽样算法,通过对两个(线性、非线性)解析函数及一组不同结构的地下水模型边缘似然值的计算,并与大样本条件下算术平均方法的计算结果相对比,验证了该方法对于计算模型边缘似然值的有效性。

The model evaluation（ model selection） is an important research content of uncertainty analysis of groundwater numerical simulation, and marginal likelihood of a model is an essential basis for model evaluation. Nested sampling algorithm is an efficient high-dimensional integral method,which can effectively calculate the marginal likelihood of complex model. The nested sampling algorithm based on Adaptive Metropolis was proposed in this study,by calculating the marginal likelihoods of two（ linear,non-linear）analytic functions and a set of groundwater models with different structures,and compared with the results of the arithmetic average method under the condition of large sample,the validity of the method was verified. The results show that the nested sampling algorithm has high calculation accuracy and computational efficiency,and is an effective model evaluation method.