Fits, and especially linear fits, with errors on both axes, extra variance of the data points and other complications
Fits, and especially linear fits, with errors on both axes, extra variance of the data points and other complications
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发表时间：
2005-11
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通讯作者：
G. D'Agostini
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作者：
G. D'Agostini
由astro-ph/0508529引起的天体物理学界的一些讨论引发了本文，其目的是从概率的角度介绍“拟合”问题（也称为贝叶斯），特别注意建立描述“依赖网络”的模型（贝叶斯网络）将实验观察与模型参数联系起来，并依赖于概率推理。详细示出了在两个轴上具有误差的线性拟合的特定情况以及直线周围的数据点的额外方差（即，不被实验误差考虑）。一些有关使用线性拟合公式对数线性化指数和幂律的问题，以及系统误差的问题。
The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the construction of model that describes the `network of dependences' (a Bayesian network) that connects experimental observations to model parameters and upon which the probabilistic inference relies. The particular case of linear fit with errors on both axes and extra variance of the data points around the straight line (i.e. not accounted by the experimental errors) is shown in detail. Some questions related to the use of linear fit formulas to log-linearized exponential and power laws are also sketched, as well as the issue of systematic errors.