贝叶斯多模型分析方法的对比研究

Comparative Study on Bayesian Multimodel Analysis Methods

多模型分析能够考虑模型本身存在的不确定性,在决策分析和风险评估中具有越来越重要的作用。对具有严谨统计分析理论基础的贝叶斯模型平均法和极大似然贝叶斯多模型平均法做了详细介绍,并改进了传统极大似然贝叶斯多模型平均法不能考虑参数不确定性的不足,使极大似然贝叶斯多模型平均法对贝叶斯模型平均法近似得更为准确。地质统计多模型对地层渗透系数的预测分析结果表明,2种多模型分析方法在参数空间确定、模型后验权重和渗透系数预测方面都具有很好的一致性。极大似然贝叶斯多模型平均法能和水文学现有的参数估计方法很好结合,且计算量小。

Multimodel analysis plays more important role in decision-making and risk assessment in recent years due to its capability to take conceptual model uncertainty into account. Two commonly used multimodel analysis methods, Bayesian model averaging method and its maximum likelihood version, are introduced. The maximum likelihood Bayesian averaging method has been improved to take parameter uncertainty into account. These methods are applied to analyze the spatial distribution of log hydraulic conductivity. The results show that these two methods are consistent with each other in terms of identifying the parameter space, determining the posterior model weights and predicting the log hydraulic conductivity distribution. The maximum likelihood Bayesian averaging method can be incorporated with the well-developed inverse modeling methods in hydrogeological researches.