Uncertainty estimation in pgopher

[BillKet]

Hello! Can someone who used pgopher before (I am fitting a diatomic molecular spectra) help me understand how does it calculate the uncertainty on the parameters when doing a line fit. I found very little online and it is not totally clear to me. Mainly I am not sure how, just by providing the relative uncertainties between different assigned lines, one can get the uncertainty on the parameters. Naively (my statistics is not great), I would imagine that if I have an uncertainty of, say, 0.1 cm$^{-1}$ on the measured transitions the error on the parameters would be much bigger compared to when I would have, say 0.0001 cm$^{-1}$ uncertainty. Yet, in pgopher, you would assign a "1" as the Std Dev parameter in both cases (i.e. you would say that all the lines have the same error), so the information about the magnitude of the errors would be gone. What am I missing?

 

[BigJDubs]

When using pgopher to fit a diatomic molecular spectrum, the uncertainty on the parameters is calculated by taking into account the relative uncertainty between different assigned lines. Specifically, the Std Dev parameter that you enter for each line indicates how much larger the uncertainty is for that line compared to the other lines. For instance, if you assign 0.0001 cm$^{-1}$ as the Std Dev for one line and 1 cm$^{-1}$ for another line, pgopher will calculate the appropriate uncertainty for each parameter based on these relative uncertainties. This means that even though you are assigning the same Std Dev value for both lines, pgopher will take into account the magnitude of the errors when calculating the uncertainty on the parameters.