Lilli S., Jeff K., Evan G.

We processed the measurements made in LHO aLOG 44766 using an MCMC to fit the data for the unknown parameters. Below are the maximum a postiori values and their 1-sigma quantiles.

Parameter                              | Quantiles (0.15, 0.50, 0.84)
---------------------------------------------------------------------
Cavity gain, H_c (ct/m)                | 3.309e+06, 3.321e+06, 3.332e+06
Cavity pole, f_cc (Hz)                 |  419, 421.7, 424.6
Detuned SRC spring frequency, f_s (Hz) | 5.54, 7.037, 8.212
Detuned SRC spring quality factor, Q_s | 66.63, 37.57, 21.87
Residual time delay, tau_c (usec)      | -3.887, -2.821, -1.734

The results are typical for what we now expect for an O3 aLIGO interferometer.

Attached are the measurement compared against the best fit model values and the corner plot output from the MCMC analysis (first and second attachments).

The final attachment is an updated Gaussian Process Regression plot showing the residuals from the Oct. 12 measurement and the Oct. 23 measurement propagated back to the Oct. 12th time. We would normally propagate the values using time dependent calibration factors derived from the calibration lines, but the front end calculation of these values is still in disarray. Since we couldn't use these values, we simply made MCMC fits to each measurement and divided out the changes that are caused because of drifts in alignment. The two sets of residuals (data points) are used in a Gaussian Process Regression algorithm to search for and quantify unknown systematic errors. The best fit using the GPR algorithm is shown as a dark line with the 1-sigma uncertainty given by the shaded region We expect that with further, higher precision measurements, the uncertainty on the GPR will be reduced.