The Bayesian method to evaluate parameter in a function is a well-known prevalenty used method for parameter estimation in many research of fields. (such as gravitational wave detector signal analysis) You can check from this link, they did a simple demonstration that Bayesian method gives a more accurate parameter estimation. In our experiment, we are trying to fit the FDS measurement result to FDS degradation model to get information of cavity detuning and homodyne angle. To achieve this goal, we were using a least square curve fit method but the error of many parameters were not considered. Therefore, to better evaluate the filter cavity detuning information, I would propose to use Bayesian method.

To do Bayesian estimation, there is a package called 'emcee' developed in python environment. The method to do this Bayesian estimation is called 'MCMC'. To use this package, we need to move the FDS degradation function from matlab to python. I did this based on the FDS code provided from Eleonora. To make sure the python function I wrote is correct, I did the comparison of python and matlab results as the  attached figure 1. I found the python code I wrote gives quite the same result with Eleonora code.

Then I made a preliminary run of the mcmc code I wrote. (It was taking ~30 hours, but can be reduced if I use parallel calculation) Based on the result of MCMC, I made a violin plot of the cavity detuning fit result estimation, as attached figure 2.

I would like to do this analysis for the future measurement of FDS.