Fechner's Law: Where Does the Log Transform Come From?

Donald Laming

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Fechner's Law: Where Does the Log Transform Come From?

机译：费希纳定律：原木变换从何而来？

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This paper looks at Fechner's law in the light of 150 years of subsequent study. In combination with the normal, equal variance, signal-detection model, Fechner's law provides a numerically accurate account of discriminations between two separate stimuli, essentially because the logarithmic transform delivers a model for Weber's law. But it cannot be taken to be a measure of internal sensation because an equally accurate account is provided by a x~2 model in which stimuli are scaled by their physical magnitude. The logarithmic transform of Fechner's law arises because, for the number of degrees of freedom, typically required in the x~2 model, the logarithm of a x~2 variable is, to a good approximation, normal. This argument is set within a general theory of sensory discrimination.

机译：本文根据150年的后续研究来研究费希纳定律。结合正常的，等方差的信号检测模型，费希纳定律在数字上准确地说明了两个单独的刺激之间的区别，这主要是因为对数变换提供了韦伯定律的模型。但是，不能将其视为内部感觉的一种度量，因为x〜2模型提供了同等准确的说明，其中刺激根据其物理大小进行缩放。费希纳定律的对数变换之所以出现，是因为对于x〜2模型中通常需要的自由度数，x〜2变量的对数是一个很好的近似值。该论点是在一般的感官歧视理论中提出的。

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《Seeing and perceiving》 |2010年第2期|共17页
作者
Donald Laming;
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正文语种 eng
中图分类生理学;
关键词
Detection; differential coupling; discrimination; Fechner's law; logarithmic transform; signal detection theory;

机译：检测;微分耦合;鉴别;费希纳定律;对数变换;信号检测理论;

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1. Fechner's Law: Where Does the Log Transform Come From? [J] . Donald Laming Seeing and perceiving . 2010,第2期

机译：费希纳定律：原木变换从何而来？
2. A Possible p-Adic Weber-Fechner Law [J] . Giuseppe Iurato P-adic numbers, ultrametric analysis and applications . 2018,第4期

机译：可能的<重点类型=“斜体”> P -Adic Weber-Fechner法
3. Determination of the flavours and marked ages of rice wines using a taste sensing system combined with the Weber-Fechner law and chemometric methods [J] . Wei ZhenBo, Wang Jun, Cui ShaoQing, Analytical methods . 2016,第33期

机译：结合Weber-Fechner定律和化学计量学方法的味道感应系统确定米酒的风味和明显的陈年
4. Sensation-growth equations for non-zero threshold sensation, evaluated using non-traditional, bounded Fechnerian integration, for Fechner's Law and for Ekman's Law, using 12 different Weber Fractions [C] . Lance Nizami International Congress and Exposition on Noise Control Engineering . 2020

机译：用于非零阈值感觉的感觉 - 增长方程，使用12种不同的韦伯分数使用非传统，有界的Fechnerian集成评估为Fechner的法律和ekman定律进行评估
5. The relationships between skinfold, fatigue and the traditional and log-transformed electromyographic and mechanomyographic signal in the vastus lateralis and recuts femoris. [D] . Cooper, Michael A. 2013

机译：皮肤皱纹，疲劳与股外侧肌中传统的和对数变换的肌电图和机械描记图信号之间的关系，并切除股骨。
6. Numerosity representations in crows obey the Weber–Fechner law [O] . Helen M. Ditz, Andreas Nieder 2016

机译：乌鸦中的云度表示服从韦伯-费希纳定律
7. Erratum: Oncogenic KRAS Regulates Tumor Cell Signaling via Stromal Reciprocation:Our paper demonstrated the cell-autonomous and non-cell-autonomous effects of oncogene signaling in tumor and stromal cells using a proteomic approach. It has come to our attention that Data S1, which summarized our proteomic and phosphoproteomic data, included two sets of errors. In the tab related to Figure 3E, the data were labeled as representing log2-transformed ratios but were erroneously formatted to represent natural ratios. These numbers have now been changed to represent log2-transformed ratios. In the tab related to Figure 5, a copying error from our proteomics software caused the 6H time values to be incorrectly displayed. These values have also now been corrected. The values represented in the corrected version of Data S1 were the ones that had been used in our analyses throughout the paper, so the conclusions and figures in the paper remain unchanged. [O] . Tape, Christopher J., Ling, Stephanie, Dimitriadi, Maria, 2016

机译：错误：致癌KRas通过基质复制调节肿瘤细胞信号：我们的论文使用蛋白质组学方法证明了肿瘤和基质细胞中癌基因信号传导的细胞自主和非细胞自主作用。我们注意到数据s1总结了我们的蛋白质组学和磷酸化蛋白质组学数据，包括两组错误。在与图3E相关的标签中，数据被标记为表示log2转换的比率，但被错误地格式化以表示自然比率。现在已将这些数字更改为表示log2转换比率。在与图5相关的选项卡中，来自我们的蛋白质组学软件的复制错误导致6H时间值被错误地显示。这些值现在也已得到纠正。数据s1的更正版本中表示的值是我们在整篇论文中用于分析的值，因此论文中的结论和数字保持不变。

Fechner's Law: Where Does the Log Transform Come From?

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