Thursday, March 14, 2013

Fitting a model to data: lit review

Yesterday I showed some preliminary TF results at our group meeting, and it was rightly noted that the straight line fit I made was wrong. I've only included errors in one variable (velocity, obtained by using bootstrapping) in the fit, and made a mess of that by mixing the variables on the plot.
I've been thinking about how to do a proper fit when the data has uncertainties in both directions, and been revisiting this paper by Hogg et al.:
In the astrophysics literature (see, for example, the Tully Fisher literature, there is a tradition, when there are uncertainties in both directions, of fi tting the "forward" and "reverse" relations, that is, fi tting y as a function of x and then x as a function of y, and then splitting the diff erence between the two slopes so obtained, or treating the di fference between the slopes as a systematic uncertainty. This is unjusti ed.

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