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MML is not Consistent for Neyman-Scott
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-04-01 , DOI: 10.1109/tit.2019.2943464
Michael Brand

Strict Minimum Message Length (SMML) is an information-theoretic statistical inference method widely cited (but only with informal arguments) as providing estimations that are consistent for general estimation problems. It is, however, almost invariably intractable to compute, for which reason only approximations of it (known as MML algorithms) are ever used in practice. Using novel techniques that allow for the first time direct, non-approximated analysis of SMML solutions, we investigate the Neyman-Scott estimation problem, an oft-cited showcase for the consistency of MML, and show that even with a natural choice of prior neither SMML nor its popular approximations are consistent for it, thereby providing a counterexample to the general claim. This is the first known explicit construction of an SMML solution for a natural, high-dimensional problem.

中文翻译:

MML 与 Neyman-Scott 不一致

严格最小消息长度 (SMML) 是一种信息论统计推理方法,被广泛引用(但仅限于非正式论据),用于提供与一般估计问题一致的估计。然而,它几乎总是难以计算,因此在实践中只使用它的近似值(称为 MML 算法)。使用首次允许对 SMML 解决方案进行直接、非近似分析的新技术,我们研究了 Neyman-Scott 估计问题,这是一个经常被引用的 MML 一致性展示,并表明即使自然选择先验SMML 及其流行的近似值都与其一致,从而为一般主张提供了反例。这是第一个已知的针对自然的 SMML 解决方案的显式构造,
更新日期:2020-04-01
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