Need an explanation for the chances in this graph

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SUMMARY

The discussion centers on the interpretation of Bayesian credible intervals as presented in the Advanced LIGO paper, specifically regarding the 90% probability range for certain values. The paper utilizes non-informative prior distributions to update parameter estimates based on observed data. Key concepts include the derivation of the chirp mass and its relation to the total mass of binary systems, as well as the identification of various noise sources affecting measurements, such as quantum noise and thermal noise.

PREREQUISITES
  • Understanding of Bayesian statistics and credible intervals
  • Familiarity with gravitational wave physics and the Advanced LIGO project
  • Knowledge of chirp mass calculations in binary systems
  • Awareness of noise types in gravitational wave detection, including quantum and thermal noise
NEXT STEPS
  • Study Bayesian statistics and its application in astrophysics
  • Learn about the derivation of chirp mass in binary systems
  • Research the impact of quantum noise on gravitational wave detectors
  • Explore the effects of thermal noise on test masses in gravitational wave observatories
USEFUL FOR

Astronomers, physicists, data analysts, and researchers involved in gravitational wave detection and analysis, particularly those interested in the statistical methods used in interpreting LIGO data.

Meerio
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In the paper Advanced LIGO they published some figures with chances. I would like to know how they know that there's a 90% chance for something to be in a specific value.

https://dcc.ligo.org/public/0122/P1500218/014/PhysRevLett.116.241102.pdf
paper here

also have some other questions:

What is a quadruple moment? (not too much terminology please)
How can you derive that from the formula, that if the chirp mass = 30 solarmasses that m1+m2 = 70 solarmasses ? (it says this in the paper with the formula for the chirp mass)
Due to what are the following noises created?

Quantum noise
Test mass thermal noise
Suspension thermal noise
Gravity gradients
 
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What the paper discusses are Bayesian credible intervals. In essence, you start by assuming some non-informative prior distribution for the parameters and see how the data modifies this distribution. You then quote the smallest range of values containing 90% of the probability.
 

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