论文标题
贝叶斯更新具有重要的采样：所需的样本量
Bayesian Update with Importance Sampling: Required Sample Size
论文作者
论文摘要
重要性抽样用于在许多计算方法中近似贝叶斯的规则，以解决贝叶斯反问题，数据同化和机器学习。本文审查并进一步研究了目标和提案之间的$χ^2 $差异的重要性样本量。我们开发了一般的摘要理论，并通过许多示例来说明尺寸，噪声级和其他模型参数在近似贝叶斯更新中具有重要性采样的作用。我们的示例还促进了对粒子过滤的标准和最佳建议的新直接比较。
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for importance sampling in terms of the $χ^2$-divergence between target and proposal. We develop general abstract theory and illustrate through numerous examples the roles that dimension, noise-level and other model parameters play in approximating the Bayesian update with importance sampling. Our examples also facilitate a new direct comparison of standard and optimal proposals for particle filtering.
