4 ms·

Thanks for doing this. I am concerned about the base rate fallacy[1] and would like to know whether/how the probability that this signal was a false positive ha

by nonbel 11y ago

Thanks for doing this. I am concerned about the base rate fallacy[1] and would like to know whether/how the probability that this signal was a false positive has been estimated. I read much discussion regarding the probability of a false alarm given the baseline model.[2] However, without an estimate of the probability of detecting a true signal during the same time frame, we cannot calculate the probability this is a false positive. Such an estimate would obviously require some prior estimates of the rate at which these black hole mergers occur and the percent that can get detected, etc. [1] https://en.wikipedia.org/wiki/Base_rate_fallacy https://en.wikipedia.org/wiki/Base_rate_fallacy [2] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.11...

nonbel 11y ago
Can someone with a reddit account link this there?
- dps1879 11y ago
  Done and done
  - dps1879 11y ago
    Some dumbass responded....they said oh so are you saying that nasa isnt perfect and didnt build a perfect detector then they actually just said "duh". So lame
topquark 11y ago
It sounds like you've already read about how we estimate the false-alarm rate for signals, so I'll just add that the estimated rate of BBH mergers was highly uncertain before this observation; the error bars spanned three orders of magnitude. See, for example, Fig 5 of http://arxiv.org/abs/1111.7314 http://arxiv.org/abs/1111.7314, which compares the previous LIGO-Virgo upper limits on similar events to the expected rate from population synthesis models and observations of high-mass X-ray binaries, known BNS systems, etc. The rate inferred from GW150914 is on the high end of the rate estimates from astronomers, but it's completely consistent with prior observations. Certainly, if we had seen ten events in the first 16 days of data, it would not have made sense! But one event is well within expectations.
- nonbel 11y ago
  Thanks, I'll have to look more closely at that paper since I only see discussion of the upper bounds. The reason for my concern is that I noted elsewhere that the prior lower bounds on the merger rates got pretty low: ~0.1 Gpc^-3 yr^-1. For only 16 days of observing the expected number of events drops to 4.38e-3 Gpc^-3. Then if the horizon distance is somewhat less than than 1 Gpc we need to scale this further. Say it was 0.5 Gpc, we scale by 0.5^3 to get ~5.475e-4 expected events. For 0.2 Gpc horizon we get ~3.5e-5! These values are getting dangerously close to the estimated background rate, at least using this crude calculation at the lower ends of the prior estimates.
- nonbel 11y ago
  A lot of this information seems to be available, for example figure 4 here[1]. According to that, the horizon distance for "a binary black hole system with the same observed spin and mass parameters as GW150914 for optimal sky location and source orientation and detected with an SNR of 8" was 1.5-2 Gpc. Now we only need an estimate of the rate at which events with these properties occur, not using the data from GW150914. I presume this is somewhat (a few orders of magnitude) less than the rate at which the mergers occur in general. [1] http://arxiv.org/abs/1602.03844 http://arxiv.org/abs/1602.03844

by nonbel 11y ago

nonbel 11y ago

Can someone with a reddit account link this there?

dps1879 11y ago
Done and done
- dps1879 11y ago
  Some dumbass responded....they said oh so are you saying that nasa isnt perfect and didnt build a perfect detector then they actually just said "duh". So lame

topquark 11y ago

It sounds like you've already read about how we estimate the false-alarm rate for signals, so I'll just add that the estimated rate of BBH mergers was highly uncertain before this observation; the error bars spanned three orders of magnitude. See, for example, Fig 5 of http://arxiv.org/abs/1111.7314 http://arxiv.org/abs/1111.7314, which compares the previous LIGO-Virgo upper limits on similar events to the expected rate from population synthesis models and observations of high-mass X-ray binaries, known BNS systems, etc. The rate inferred from GW150914 is on the high end of the rate estimates from astronomers, but it's completely consistent with prior observations. Certainly, if we had seen ten events in the first 16 days of data, it would not have made sense! But one event is well within expectations.

nonbel 11y ago
Thanks, I'll have to look more closely at that paper since I only see discussion of the upper bounds. The reason for my concern is that I noted elsewhere that the prior lower bounds on the merger rates got pretty low: ~0.1 Gpc^-3 yr^-1. For only 16 days of observing the expected number of events drops to 4.38e-3 Gpc^-3. Then if the horizon distance is somewhat less than than 1 Gpc we need to scale this further. Say it was 0.5 Gpc, we scale by 0.5^3 to get ~5.475e-4 expected events. For 0.2 Gpc horizon we get ~3.5e-5! These values are getting dangerously close to the estimated background rate, at least using this crude calculation at the lower ends of the prior estimates.
nonbel 11y ago
A lot of this information seems to be available, for example figure 4 here[1]. According to that, the horizon distance for "a binary black hole system with the same observed spin and mass parameters as GW150914 for optimal sky location and source orientation and detected with an SNR of 8" was 1.5-2 Gpc. Now we only need an estimate of the rate at which events with these properties occur, not using the data from GW150914. I presume this is somewhat (a few orders of magnitude) less than the rate at which the mergers occur in general. [1] http://arxiv.org/abs/1602.03844 http://arxiv.org/abs/1602.03844