论文标题
非线性问题的集合卡尔曼反转：权重，一致性和方差界限
Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds
论文作者
论文摘要
集合Kalman倒置（ENKI）和集合平方根滤波器（ENSRF）是获取目标后验分布的流行抽样方法。在数据同化方法集合Kalman滤波器中，它们似乎是一个步骤（分析步骤）。尽管它们很受欢迎，但是当前向地图是非线性时，它们并不是公正的。另一方面，重要的采样（IS）以较大的权重差异获得了无偏的采样，从而导致高力矩收敛缓慢。 我们建议Wenki和Wensrf，本文中Enki和Ensrf的加权版本。它遵循与重量校正的Enki/EnsRF相同的梯度流。与经典方法相比，新方法是公正的，并且与IS相比，该方法的权重方差有界。本文将严格证明这两种属性。我们进一步讨论了基本的fokker-planck方程的稳定性。这部分解释了为什么Enki尽管不一致，但在非线性设置中偶尔表现良好。最终将证明数值证据。
Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (the analysis step) in the data assimilation method Ensemble Kalman Filter. Despite their popularity, they are, however, not unbiased when the forward map is nonlinear. Important Sampling (IS), on the other hand, obtains the unbiased sampling at the expense of large variance of weights, leading to slow convergence of high moments. We propose WEnKI and WEnSRF, the weighted versions of EnKI and EnSRF in this paper. It follows the same gradient flow as that of EnKI/EnSRF with weight corrections. Compared to the classical methods, the new methods are unbiased, and compared with IS, the method has bounded weight variance. Both properties will be proved rigorously in this paper. We further discuss the stability of the underlying Fokker-Planck equation. This partially explains why EnKI, despite being inconsistent, performs well occasionally in nonlinear settings. Numerical evidence will be demonstrated at the end.
