贝叶斯后验分布高斯过程近似的后验一致性
数值分析
2024-10-01 v3 数值分析
摘要
我们研究使用高斯过程仿真器来近似贝叶斯逆问题中的参数到观测映射或负对数似然。我们证明了真实后验分布与基于高斯过程仿真器的各种近似之间的 Hellinger 距离上的误差界。我们的分析包括基于预测过程均值的近似，以及基于完整高斯过程仿真器的近似。我们的结果表明，真实后验与其近似之间的 Hellinger 距离可由仿真器误差的矩来界定。数值结果证实了我们的理论发现。
引用
@article{arxiv.1603.02004,
title = {Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions},
author = {Andrew M. Stuart and Aretha L. Teckentrup},
journal= {arXiv preprint arXiv:1603.02004},
year = {2024}
}
备注
In the latest version, we have added Assumption A. This is required in the proofs of Corollaries 4.3, 4.10 and 4.12, and we would like to thank Holger Wendland for alerting us of this omission. The latest version further corrects the definition of X at the beginning of section 2