Vieland V J, Das J, Hodge S E, Seok S-C
Battelle Center for Mathematical Medicine, The Research Institute at Nationwide Children's Hospital and The Ohio State University, 575 Children's Crossroad, Columbus, OH 43215, USA.
Theory Biosci. 2013 Sep;132(3):181-94. doi: 10.1007/s12064-013-0180-9. Epub 2013 Mar 5.
Statistical analysis is used throughout biomedical research and elsewhere to assess strength of evidence. We have previously argued that typical outcome statistics (including p values and maximum likelihood ratios) have poor measure-theoretic properties: they can erroneously indicate decreasing evidence as data supporting an hypothesis accumulate; and they are not amenable to calibration, necessary for meaningful comparison of evidence across different study designs, data types, and levels of analysis. We have also previously proposed that thermodynamic theory, which allowed for the first time derivation of an absolute measurement scale for temperature (T), could be used to derive an absolute scale for evidence (E). Here we present a novel thermodynamically based framework in which measurement of E on an absolute scale, for which "one degree" always means the same thing, becomes possible for the first time. The new framework invites us to think about statistical analyses in terms of the flow of (evidential) information, placing this work in the context of a growing literature on connections among physics, information theory, and statistics.
统计分析在生物医学研究及其他领域被广泛用于评估证据强度。我们之前曾指出，典型的结果统计量（包括p值和最大似然比）具有较差的测度理论性质：随着支持某一假设的数据不断积累，它们可能会错误地表明证据在减少；而且它们无法进行校准，而校准对于跨不同研究设计、数据类型和分析水平进行有意义的证据比较是必要的。我们之前还提出，热力学理论首次实现了温度（T）绝对测量尺度的推导，可用于推导证据（E）的绝对尺度。在此，我们提出一个全新的基于热力学的框架，在这个框架中，首次有可能以绝对尺度测量E，对于该绝对尺度而言，“一度”始终具有相同的含义。这个新框架促使我们从（证据）信息流的角度思考统计分析，将这项工作置于关于物理学、信息论和统计学之间联系的不断增长的文献背景中。
