Timeline for How to perform a multi-peak fitting?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2016 at 3:17 | comment | added | Silvia | @TomWenseleers Nice! Thanks for sharing it to me! | |
| Jan 5, 2016 at 12:56 | comment | added | Tom Wenseleers | You could also determine n based on the Aikaike Information Criterion AIC or the Bayesian Information Criterion BIC, as in this post: mathematica.stackexchange.com/questions/94154/…, as that would penalize higher nrs of estimated parameters | |
| Aug 23, 2013 at 6:33 | vote | accept | Everett You | ||
| Jun 7, 2013 at 2:59 | comment | added | Silvia | @KennyColnago Yes that is what I mean to introduce the penalty function. But I think it actually depends. Sometimes people care more about the accurate number of peaks, sometimes they care more about the goodness-of-fit. Maybe there should be an adjustable leverage parameter for the end-user? | |
| Jun 7, 2013 at 2:58 | comment | added | J. M.'s missing motivation♦ | @Kenny, ah, that's a much better formulation. Indeed, if adding the $n+1$-th term does not change $\chi^2$ much, then one can comfortably settle for the $n$-term model. | |
| Jun 7, 2013 at 2:43 | comment | added | KennyColnago | @J.M. In the absence of numerical problems, shouldn't $\chi^2$ keep decreasing as $n$ increases? More parameters make for fits with smaller residuals? Perhaps, like an F test, $n$ should be chosen as the max value such that $\chi^2$ does not significantly decrease (whatever significantly means). | |
| Jun 6, 2013 at 14:55 | comment | added | J. M.'s missing motivation♦ | One might consider designing a method built on top of Silvia's proposal: starting from an initial estimate of $n$, do the fitting and note the $\chi^2$ value. Increment $n$, fit again, and see if $\chi^2$ decreases. Keep doing this until you see an increase in $\chi^2$, and then keep the fit that had the least value of $\chi^2$. | |
| Jun 6, 2013 at 5:33 | comment | added | Silvia | @EverettYou You're welcome. I think the penalty function design is straightforward from the phenomenon I shew. I know you're a student, I think this remaining problem would be a good exercise on scientific numerical computing. | |
| Jun 6, 2013 at 4:38 | comment | added | Everett You | Thanks for the great answer. How to design the penalty function? Something proportional to $n$, or any other functions? | |
| Jun 4, 2013 at 9:26 | history | edited | Silvia | CC BY-SA 3.0 |
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| Jun 4, 2013 at 6:08 | history | answered | Silvia | CC BY-SA 3.0 |