Issues concerning dequatorial_radius interval using fit_ellipse() method

[Raph65]

Hello,
I am doing an ellipse fitting for a 5 positive occultation observations. I am trying to fit an ellipse using the fit_ellipse() method on sora.occultation but depending on the optimization method used I have a different result regarding the equatorial radius.
I fixed equatorial_radius = 2410.3 km and dequatorial_radius = 1.5 km

Results using "least_square" or "differential_evolution" method:

equatorial_radius:
1-sigma: 2407.325 +/- 0.000
3-sigma: 2407.418 +/- 0.105

Here the result is out of the given interval [2408.8,2411.8]

Results using "chisqr" method:

equatorial_radius:
1-sigma: 2408.824 +/- 0.023
3-sigma: 2408.908 +/- 0.108

Can we explain this difference by scipy_optimization methods (used in least_square and differential_evolution methods)?

Thanks

[rcboufleur]

Hi Raph65,

There is a fundamental difference between chisqr and the methods based on SciPy. The 'chisqr' approach relies on Monte Carlo simulations, meaning that with a sufficient number of iterations or guesses, you can achieve a value similar to what would be obtained using the convergence techniques employed by SciPy's least_squares and differential_evolution methods. While 'chisqr' provides a probabilistic approximation through repeated random sampling, SciPy's methods use deterministic algorithms to systematically converge on an optimal solution.

However, it's important to note that while the convergence methods are effective in finding the best solution, 'chisqr' is still used to compute the error bars. Therefore, when using this approach, it's crucial to carefully consider the appropriate range for parameters, especially since some error bars might be too small, potentially leading to inaccurate interpretations.

For questions like these, please feel free to use our Slack channel. For software-related issues, we prefer that you raise them via GitHub issues.

[Raph65]

HI Rodrigo, Thanks for your quick answer, I understand know. It s then better to adapt parameters to use « ls » or « de » methods even if they are not physically accurate at the beginning ? Concerning the Slack channel thank you for sharing and sorry for the confusion, do you want me to delete my question on Github it is not a problem for me. Sincerely, Raphaël

…

Le 12 août 2024 à 16:13, Rodrigo Boufleur ***@***.***> a écrit : Hi Raph65, There is a fundamental difference between chisqr and the methods based on SciPy. The 'chisqr' approach relies on Monte Carlo simulations, meaning that with a sufficient number of iterations or guesses, you can achieve a value similar to what would be obtained using the convergence techniques employed by SciPy's least_squares and differential_evolution methods. While 'chisqr' provides a probabilistic approximation through repeated random sampling, SciPy's methods use deterministic algorithms to systematically converge on an optimal solution. However, it's important to note that while the convergence methods are effective in finding the best solution, 'chisqr' is still used to compute the error bars. Therefore, when using this approach, it's crucial to carefully consider the appropriate range for parameters, especially since some error bars might be too small, potentially leading to inaccurate interpretations. For questions like these, please feel free to use our Slack channel <https://join.slack.com/t/sora-grupo/shared_invite/zt-16cuhoa81-oX29_r78RQX1WefKaeeTwg>. For software-related issues, we prefer that you raise them via GitHub issues. — Reply to this email directly, view it on GitHub <#92 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/BFF3K4O5NM3RDY2VNUE2MODZRC7JZAVCNFSM6AAAAABMMHHZG2VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDEOBUGEYDEMZSGI>. You are receiving this because you authored the thread.

[rcboufleur]

Hi Raphaël,

I’m not entirely sure I fully grasp your question, but here are my thoughts on when each method might be more appropriate. Convergence methods, like least_squares and differential_evolution, are generally much faster than Monte Carlo simulations. However, they can sometimes get stuck in local minima during the convergence process. While this is rare in the context of SORA, it could happen with lower-quality data. Despite this, these methods are usually the most straightforward way to find the best-fit parameters.

On the other hand, the chisqr method has the advantage of always finding the best-fit region, though it comes at the cost of longer computation times. Additionally, it’s used to estimate the uncertainty in the parameters, which provides context for how meaningful the best fit is, regardless of the method used.

So, a combination of both approaches might be the most efficient choice. Experimenting with both methodologies could also give you a better perspective on which is more suitable for your specific case, especially when analyzing the chi-square maps that are generated.

As for your GitHub question, there’s no need to delete it. It’s valuable for the community and might help others who have similar inquiries.

[Raph65]

Thank you for your reply, these clarifications are indeed important. I've clearly understood the importance of using the complementarity of the two methods to be able to derive the parameters of the ellipse in the best way. I'm sorry if I didn't word my question properly, but what particularly bothered me about the difference between stochastic and deterministic methods was the respect of the intervals given as input. Here in my example, the deterministic methods returned a result outside this interval [2408.8;2411.8] for the equatorial radius. Is it the nature of these methods, and in particular the fact that they converge towards a local minimum, that gives me such an "unexpected" result? Or is it not so unexpected and I am missing something? Thanks a lot<;

…

Le 12 août 2024 à 16:59, Rodrigo Boufleur ***@***.***> a écrit : Hi Raphaël, I’m not entirely sure I fully grasp your question, but here are my thoughts on when each method might be more appropriate. Convergence methods, like least_squares and differential_evolution, are generally much faster than Monte Carlo simulations. However, they can sometimes get stuck in local minima during the convergence process. While this is rare in the context of SORA, it could happen with lower-quality data. Despite this, these methods are usually the most straightforward way to find the best-fit parameters. On the other hand, the chisqr method has the advantage of always finding the best-fit region, though it comes at the cost of longer computation times. Additionally, it’s used to estimate the uncertainty in the parameters, which provides context for how meaningful the best fit is, regardless of the method used. So, a combination of both approaches might be the most efficient choice. Experimenting with both methodologies could also give you a better perspective on which is more suitable for your specific case, especially when analyzing the chi-square maps that are generated. As for your GitHub question, there’s no need to delete it. It’s valuable for the community and might help others who have similar inquiries. — Reply to this email directly, view it on GitHub <#92 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/BFF3K4KDB6WYOPNAMZZASZ3ZRDEVNAVCNFSM6AAAAABMMHHZG2VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDEOBUGIYTMMJUGM>. You are receiving this because you authored the thread.

[rcboufleur]

Hi Raphaël,

That does indeed sound like strange behavior, especially if the case is with the differential_evolution method that by design only works if bounds are provided. Please reach out to me in the Slack channel so I can provide more specific support for your case.