Bayesian Consistency with the Supremum Metric

• URL: http://arxiv.org/abs/2201.03447v1
• Date: Mon, 10 Jan 2022 16:39:25 GMT
• Title: Bayesian Consistency with the Supremum Metric
• Abstract summary: A key result of the paper is that we demonstrate supremum consistency using weaker conditions compared to those currently used to secure $mathbbL_1$ consistency.
• Score: 13.769786711365104
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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