SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 1, Page 114-138, January 2020.
A vital stage in the mathematical modeling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as approximate Bayesian computation (ABC), build Monte Carlo samples of the uncertain parameter distribution by comparing the data with large numbers of model simulations. However, the computational expense of generating these simulations forms a significant bottleneck in the practical application of such methods. We identify how simulations of corresponding cheap, low-fidelity models have been used separately in two complementary ways to reduce the computational expense of building these samples, at the cost of introducing additional variance to the resulting parameter estimates. We explore how these approaches can be unified so that cost and benefit are optimally balanced, and we characterize the optimal choice of how often to simulate from cheap, low-fidelity models in place of expensive, high-fidelity models in Monte Carlo ABC algorithms. The resulting early accept/reject multifidelity ABC algorithm that we propose is shown to give improved performance over existing multifidelity and high-fidelity approaches.

中文翻译：

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多保真近似贝叶斯计算

SIAM / ASA不确定性量化期刊，第8卷，第1期，第114-138页，2020年1月。
在实际系统的数学建模中，至关重要的一步是将模型的参数校准为观测数据。诸如近似贝叶斯计算（ABC）的无可能性参数推断方法通过将数据与大量模型仿真进行比较来构建不确定参数分布的蒙特卡洛样本。但是，生成这些模拟的计算费用在此类方法的实际应用中形成了很大的瓶颈。我们确定了如何以两种互补的方式分别使用相应的廉价，低保真度模型的仿真，以减少构建这些样本的计算量，但以对结果参数估计值引入额外方差为代价。我们探索如何统一使用这些方法，以使成本和收益达到最佳平衡，我们在蒙特卡洛ABC算法中表征了从廉价，低保真度模型代替昂贵，高保真度模型进行仿真的频率的最佳选择。我们提出的最终的早期接受/拒绝多保真ABC算法显示出比现有的多保真和高保真方法更高的性能。