| Re: getting derivatives from spline [message #66029] |
Tue, 14 April 2009 05:50  |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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On Apr 13, 12:54 pm, jameskuyper <jameskuy...@verizon.net> wrote:
> Jeremy Bailin wrote:
>> Does anyone know a way of getting SPLINE or any of its friends to
>> return the derivatives of the interpolating function at the desired
>> abscissae in addition to the interpolated values?
>
>> Or, another way of getting at this question: what is everyone's
>> favourite algorithm for numerically calculating the derivatives of
>> (slightly) noisy data?
>
> Don't use splines to fit noisy data. The spline treats the noise as
> being just as real as the signal. Particularly with higher-order
> splines, it's easy to end up with interpolated data which looks even
> noisier than the raw data.
>
> Instead, fit the noisy data to a model with fewer free parameters than
> you have data points. The difference between the number of data points
> and the number of free parameters is a measure of the amount of
> information you're discarding. If you've made a good choice of model,
> the information you're discarding will be about the noise; with a bad
> model, you'll be discarding information about the signal. Choosing the
> right model for your data is therefore a key step in this process.
>
> The fundamental problem with using splines is that the number of data
> points is the same as the number of free parameters - you aren't
> discarding any noise.
In the long run, that's obviously the correct thing to do. But I was
trying to see if I can come up with a quick way of getting an idea of
what the differential distribution of a quantity looks like given its
cumulative distribution, where the "noise" is really just coming from
the fact that the distribution isn't sampled that well in the tail.
In other words, what I'm really looking for is a quick way of doing an
adaptively-binned differential distribution. Which, now that I express
it like that, is easier than screwing around with getting derivatives
out of a fit to the cumulative distribution, so I'll just go ahead and
do that!
-Jeremy.
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