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 Wed May 13 18:07:32 2020, anchal, DailyProgress, NoiseBudget, Bayesian Analysis Fri May 15 12:09:17 2020, aaron, DailyProgress, NoiseBudget, Bayesian Analysis Fri May 15 16:50:24 2020, anchal, DailyProgress, NoiseBudget, Bayesian Analysis Fri May 22 17:22:37 2020, anchal, DailyProgress, NoiseBudget, Bayesian Analysis Mon May 25 08:54:26 2020, anchal, DailyProgress, NoiseBudget, Bayesian Analysis with Hard Ceiling Condition Tue May 26 15:45:18 2020, anchal, DailyProgress, NoiseBudget, Bayesian Analysis Thu May 28 14:13:53 2020, anchal, DailyProgress, NoiseBudget, Bayesian Analysis Sun May 31 11:44:20 2020, Anchal, DailyProgress, NoiseBudget, Bayesian Analysis Finalized Mon Jun 1 11:09:09 2020, rana, DailyProgress, NoiseBudget, Bayesian Analysis Finalized Thu Jun 4 09:18:04 2020, Anchal, DailyProgress, NoiseBudget, Bayesian Analysis Finalized Thu Jun 11 14:02:26 2020, Anchal, DailyProgress, NoiseBudget, Bayesian Analysis Finalized Mon Jun 15 16:43:58 2020, Anchal, DailyProgress, NoiseBudget, Better measurement on June 14th Tue Jun 23 17:28:36 2020, Anchal, DailyProgress, NoiseBudget, Better measurement on June 22nd (as I turned 26!) Wed Jun 24 21:14:58 2020, Anchal, DailyProgress, NoiseBudget, Better measurement on June 24th Fri Jun 26 12:38:34 2020, Anchal, DailyProgress, NoiseBudget, Bayesian Analysis Finalized, Adding Slope of Bulk Loss Angle as variable
Message ID: 2572     Entry time: Fri May 15 12:09:17 2020     In reply to: 2571     Reply to this: 2573
 Author: aaron Type: DailyProgress Category: NoiseBudget Subject: Bayesian Analysis

Wow, very suggestive ASD. A couple questions/thoughts/concerns:

• It's typically much easier to overestimate than underestimate the loss angle with a ringdown measurement (eg, you underestimated clamping loss and thus are not dominated by material dissipation). So, it's a little surprising that you would find a higher loss angle than Penn et all. That said, I don't see a model uncertainty for their dilution factors, which can be tricky to model for thin films.
• If you're assuming a flat prior for bulk loss, you might do the same for shear loss. Since you're measuring shear losses consistent with zero, I'd be interested to see how much if at all this changes your estimate.
• I'm also surprised that you aren't using the measurements just below 100Hz. These seem to have a spectrum consistent with brownian noise in the bucket between two broad peaks. Were these rejected in your cleaning procedure?
• Is your procedure for deriving a measured noise Gaussian well justified? Why assume Gaussian measurement noise at all, rather than a probability distribution given by the measured distribution of ASD?
• It's not clear to me where your estimated Gaussian is coming from. Are you making a statement like "given a choice of model parameters \phi_bulk and \phi_shear, the model predicts a measured ASD at frequency f_m will have mean \mu_m and standard deviation \sigma_m"?
• I found taking a deep dive into Feldman Cousins method for constructing frequentist confidence intervals highly instructive for constructing an unbiased likelihood function when you want to exclude a nonphysical region of parameter space. I'll admit both a historical and philosophical bias here though :)
• Can this method ever reject the hypothesis that you're seeing Brownian noise? I don't see how you could get any distribution other than a half-gaussian peaked at the bulk loss required to explain your noise floor.
• I think you instead want to construct a likelihood function that tells you whether your noise floor has the frequency dependence of Brownian noise.
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