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2010

Dos and don'ts of reduced chi-squared

Andrae, Rene, Schulze-Hartung, Tim, Melchior, Peter

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Reduced chi-squared is a very popular method for model assessment, model comparison, convergence diagnostic, and error estimation in astronomy.

In this manuscript, we discuss the pitfalls involved in using reduced chi-squared.
There are two independent problems: (a) The number of degrees of freedom can only be estimated for linear models.
Concerning nonlinear models, the number of degrees of freedom is unknown, i.e., it is not possible to compute the value of reduced chi-squared.

Dos and don'ts of reduced chi-squared · Around

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Smirnov, N. 1948, Annals of Mathematical Statistic, 19, 279
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Barlow, R. 1993, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (Wiley VCH)
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Then

Mayor, M., Bonfils, X., Forveille, T., et al. 2009, A&A, 507, 487
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Later among the works it cites.
Andrae, R. 2010, ArXiv e-prints 1009.2755
2010
Closest in time.
Vogt, S. S., Butler, R. P., Rivera, E. J., et al. 2010, ApJ, 723, 954
2010
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