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Data analysis recipes: Fitting a model to data · Around

2010

Data analysis recipes: Fitting a model to data

Hogg, David W., Bovy, Jo, Lang, Dustin

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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.

Built on

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Isobe, T., Feigelson, E. D., Akritas, M. G., & Babu, G. J., 1990, Linear regression in astronomy, Astrophysical Journal
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Gilks, W. R., Richardson, S., & Spiegelhalter, D., 1995, Markov chain Monte Carlo in practice: interdisciplinary statistics
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Press, W. H., 1997, Understanding data better with Bayesian and global statistical methods, in Unsolved problems in astrophysics,
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Then

Kelly, B. C., 2007, Some aspects of measurement error in linear regression of astronomical data, Astrophysical Journal
2007
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Bovy, J., Hogg, D. W., & Roweis, S. T., 2009, Extreme deconvolution: inferring complete distribution functions from noisy, heterogeneous, and incomplete observations, arXiv:0905.2979 [stat.ME]
Original
2009
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