Sometimes Size Does Not Matter

Recently Díaz, Hössjer and Marks (DHM) presented a Bayesian framework to measure cosmological tuning (either fine or coarse) that uses maximum entropy (maxent) distributions on unbounded sample spaces as priors for the parameters of physical models ( https://doi.org/10.1088/1475-7516/2021/07/020 ). The DHM stands in contrast previous attempts rely uniform prior assumption. However, since often take values infinite size, uniformity assumption is unwarranted. This known normalization problem. In this paper we explain why how not only evades problem but also circumvents other objections measurement like so called weak anthropic principle, selection single maxent distribution and, importantly, lack invariance with respect data transformations. We propose treat fine-tuning an emergence avoid loops hyperparameters (common all analysis), using are particular cases framework. Finally, prove theorem, explaining when coarse different families distributions. theorem summarized table ease reference, three analyzed conclusions theorem.