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arXiv · 2201.03447

Bayesian Consistency with the Supremum Metric

Nhat Ho·Stephen G. Walker
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Abstract

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.

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Nhat Ho, Stephen G. Walker. 2022-01-10. Bayesian Consistency with the Supremum Metric. https://arxiv.org/abs/2201.03447

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