论文标题
贝叶斯与超级公制的一致性
Bayesian Consistency with the Supremum Metric
论文作者
论文摘要
我们介绍了贝叶斯在高级公制中的一致性的简单条件。该技术的关键是三角形不平等，它使我们能够明确使用弱收敛，这是标准kullback的结果 - 先验的Leibler支持条件。另一个条件是确保密度平滑版本距离原始密度不远，从而处理可能过于紧密跟踪数据的密度。本文的一个关键结果是，与当前用于保护$ \ Mathbb {l} _1 $一致性的条件相比，我们使用较弱的条件证明了最高的一致性。
We present simple conditions for Bayesian consistency in the supremum metric. The key to the technique is a triangle inequality which allows us to explicitly use weak convergence, a consequence of the standard Kullback--Leibler support condition for the prior. A further condition is to ensure that smoothed versions of densities are not too far from the original density, thus dealing with densities which could track the data too closely. A key result of the paper is that we demonstrate supremum consistency using weaker conditions compared to those currently used to secure $\mathbb{L}_1$ consistency.
