数据分析方法：将模型拟合到数据
Data analysis recipes: Fitting a model to data
摘要：
我们将介绍在将模型拟合到数据时所涉及的许多考虑因素，以将一条直线拟合到二维平面中的一组点为例。标准加权最小二乘拟合仅适用于以下情况：存在一个维度，沿该维度数据点具有可忽略的不确定性，并且另一个维度，沿该维度所有不确定性可以由已知方差的高斯描述;这些条件在实践中很少满足。我们考虑的情况下，一般的，异质的，任意协变的二维不确定性，以及在其中有坏数据（大离群值），未知的不确定性，未知的，但预期的内在分散的线性关系拟合的情况。最重要的是，我们强调为数据建立一个“生成模型”的重要性，即使是一个近似模型。一旦存在生成模型，则随后的拟合是非任意的，因为该模型允许直接计算参数的似然性或后验概率分布。如果有“讨厌的参数”要边缘化掉，则后验概率分布的构造是必不可少的。
英文摘要：
We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted least-squares fitting is only appropriate when there is a dimension along which the data points have negligible uncertainties, and another along which all the uncertainties can be described by Gaussians of known variance; these conditions are rarely met in practice. We consider cases of general, heterogeneous, and arbitrarily covariant two-dimensional uncertainties, and situations in which there are bad data (large outliers), unknown uncertainties, and unknown but expected intrinsic scatter in the linear relationship being fit. Above all we emphasize the importance of having a "generative model" for the data, even an approximate one. Once there is a generative model, the subsequent fitting is non-arbitrary because the model permits direct computation of the likelihood of the parameters or the posterior probability distribution. Construction of a posterior probability distribution is indispensible if there are "nuisance parameters" to marginalize away.
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