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AAVSO / VStar

VStar is a visualisation and analysis tool for variable star data brought to you by AAVSO
https://www.aavso.org/vstar
GNU Affero General Public License v3.0
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Time error estimate of minimum or maximum from a polynomial fit #258

Open dbenn opened 2 years ago

dbenn commented 2 years ago

See Roy Axelson's request here: https://www.aavso.org/comment/162089#comment-162089

dbenn commented 2 years ago

Grant Foster's light curve analysis book briefly talks about uncertainty of minima/maxima when using a model, such as binned means or polynomials, but unlike his treatment of period error for which standard error of the frequency and FWHM are suggested, there is not a similar concrete suggestion for polynomials fits.

dbenn commented 2 years ago

This overview of methods by Tom Richards of Variable Stars South focusses on polynomial fitting and Kwee van Woerden and on balance seems to favour polynomials, especially low order polynomials:

https://www.variablestarssouth.org/wp-content/uploads/2020/01/nl_2020-1.pdf

It emphasises the importance of estimating "...which order of polynomial fits best without over-fitting, and what does that do for the vital polynomial curve-fit to minimum" (which VStar already provides, via RMS, AIC, BIC goodness of fit measures) and minima/maxima error estimates but doesn't examine that in any detail at least for polynomial fits. It also suggests the utility of a suite of methods, as found in Bob Nelson's Minima 25.

What's needed is equations, algorithms or source code though.

dbenn commented 2 years ago

This paper (via Brad Walter, who has pointed to a number of papers including Kwee van Woerden related papers) is useful re: polynomial extrema uncertainty:

https://www.researchgate.net/publication/227023900_On_Methods_for_the_Light_Curves_Extrema_Determination

See the equation in Section 2, page 2.

It makes sense that if the extrema determination method is derivative based, the uncertainty must be in terms of this.

Question: Could the term in the numerator simply be based upon the time resolution of the first derivative based extrema determination?

dbenn commented 2 years ago

See also https://www.aavso.org/tmaxmin which also provides some commentary on this, including mention of Bob Nelson's Minima software.

I also want to make note of the passing of Bob Nelson on November 2 2022 (3 days ago).