| Re: reading old code... why would one do this? [message #68456] |
Thu, 22 October 2009 16:47  |
wallabadah
Messages: 28
Registered: November 2005
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Junior Member |
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On Oct 23, 10:07 am, Chris <beaum...@ifa.hawaii.edu> wrote:
> On Oct 22, 11:36 am, wallabadah <write.to.wpow...@gmail.com> wrote:
>
>
>
>
>
>> Hi All,
>
>> I'm in the process of reviewing and rewriting some old routines I
>> inherited... and I've come across the following code snippet:
>
>> a = svdfit(x, y, fitting_order + 1, measure_errors = e, $
>> variance = var, chisq = c)
>> ; this line added to give results consistent with IDL pre 5.4
>> var = var * c
>
>> I'm a bit worried about the last line - I don't have access to IDL
>> documentation pre version 6.1, so I have two questions...
>> - was there some change in the output of svdfit that would require
>> such an 'adjustment' of the variance value?
>> - if not - maybe the statistics gurus can tell me if variance * chisq
>> has some mystical statistical meaning that I'm missing
>
>> cheers,
>
>> Will.
>
> [begin speculation]
>
> When fitting lines, the error bars (i.e. the variance) of the fitted
> parameters (slope and intercept) are determined entirely by the error
> bars in the individual data points. The scatter of those data points
> about the line is not considered, because the process assumes that the
> data's error bars accurately describe the amount of scatter. If this
> assumption is wrong (i.e. the data points have incorrect error bars)
> this manifests itself as an inappropriately high chi-squared value.
>
> When the error bars are the correct size, the REDUCED chi squared (chi
> squared / number of data points) should be near one. If the value was
> 2, for example, that suggests that the data's error bars were too
> small by a factor of 2-ish, given their intrinsic scatter. Some people
> use this number to adjust the error bars on the individual data points
> (make them 2x bigger) which (i think) has the effect of making the
> fitted parameter error bars bigger by the same factor. It's not a
> super-kosher approach, since something may be wrong with the data or
> model assumptions if reduced chi-squared is much different than one.
>
> However, that doesn't really explain what's going on with your code,
> since the variance is being multiplied by the unreduced chi-squared
> value. That just seems wrong. And I dont know what the deal is with
> the compatibility comment.
>
> [end speculation]
>
> Chris
Thanks Chris, such speculation is just what I require - not easy to
find in any textbook! The errors in the individual data points come
from poisson or counting statistics - I don't see any reason to
suspect they're incorrect, but I'll have a look at the reduced chi-
squared numbers...
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