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Abstract: 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 atwo-dimensional plane. Standard weighted least-squares fitting is onlyappropriate when there is a dimension along which the data points havenegligible uncertainties, and another along which all the uncertainties can bedescribed by Gaussians of known variance; these conditions are rarely met inpractice. We consider cases of general, heterogeneous, and arbitrarilycovariant two-dimensional uncertainties, and situations in which there are baddata large outliers, unknown uncertainties, and unknown but expectedintrinsic scatter in the linear relationship being fit. Above all we emphasizethe importance of having a -generative model- for the data, even an approximateone. Once there is a generative model, the subsequent fitting is non-arbitrarybecause the model permits direct computation of the likelihood of theparameters or the posterior probability distribution. Construction of aposterior probability distribution is indispensible if there are -nuisanceparameters- to marginalize away.



Author: David W. Hogg NYU, MPIA, Jo Bovy NYU, Dustin Lang Toronto, Princeton

Source: https://arxiv.org/







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