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I am interested in learning (and implementing) an alternative to polynomial interpolation.

However, I am having trouble finding a good description of how these methods work, how they relate, and how they compare.

I would appreciate your input on the pros/cons/conditions under which these methods or alternatives would be useful, but some good references to texts, slides, or podcasts would be sufficient.

note: I asked this question on stats.SE a few weeks ago and received the recommendation to ask here since I have not received an answer.

Thanks!

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    In a nutshell: use splines if your curve has to pass through the given data (with the implicit assumption that your data is "exact"), and use smoothing splines if you have "noisy" data and you want to get a feel for how the data varies. FWIW, my opinion is that smoothing data for purposes of display is cheating; show the noisy data, and figure out why your data is noisy to begin with instead of being content with smoothing.2010-12-14
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    @J.M. thank you for your explanation - would be a good answer. Wouldn't it be okay to present both the data and the smoothed curve? In my case, I am trying to approximate a complex deterministic function (a dynamic vegetation model), and have been fitting a spline - this works nicely but the use of gaussian process emulators was also suggested to me.2010-12-14
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    I'm not being mathematically rigorous here, so I left that as a comment instead. If indeed you'll be showing both the data points and the smoothed spline, then that's okay; as I said, the smoothing spline is useful for displaying trend(s), but please please do **not** use the smoothed spline to derive anything of statistical significance from your data! As for GPEs, I've not used them in my line of work so I can't really say anything about them.2010-12-14

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