论文标题
非参数状态和漂移估计的后部收缩率
Posterior contraction rates for non-parametric state and drift estimation
论文作者
论文摘要
我们考虑线性随机热方程的组合状态和漂移估计问题。无限维贝叶斯推论问题是根据Kalman-Bucy滤波器在扩展状态空间上提出的，并研究了其长期的渐近性能。未知漂移功能中渐近后收缩率是本文的主要贡献。在固定的非参数贝叶斯逆问题之前已经对这种速率进行了研究，在这里，我们证明了我们时间依赖的公式的一致性，这些先前的结果在尺度分离和缓慢的歧管近似方面构建了这些结果。
We consider a combined state and drift estimation problem for the linear stochastic heat equation. The infinite-dimensional Bayesian inference problem is formulated in terms of the Kalman-Bucy filter over an extended state space, and its long-time asymptotic properties are studied. Asymptotic posterior contraction rates in the unknown drift function are the main contribution of this paper. Such rates have been studied before for stationary non-parametric Bayesian inverse problems, and here we demonstrate the consistency of our time-dependent formulation with these previous results building upon scale separation and a slow manifold approximation.
