Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inference

תקציר מקורי באנגליתarXiv:2606.27090v2 Announce Type: replace-cross Abstract: Global objectives, such as KL divergence and ELBO, are widely used in Bayesian inference for measuring distributional discrepancy. This paper studies distributional ``local-mass behaviours'' that are not directly captured by such global objectives. We introduce and use two mathematical tools: (1) Mass Index for recording the polynomial and logarithmic decay scales of local mass, and (2) regularised extended KL (RE-KL), a set-localised divergence that can be formulated in the presence of singular components. Mass Indices help characterise how Bayesian updating changes local mass: (1) power-log likelihood factors shift it explicitly, and (2) parameter-dependent supports, or their smooth softenings, may change the local scale through t