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The reported discovery of gravitational waves has been put in question by the scientific community:

https://www.quantamagazine.org/strange-noise-in-gravitational-wave-data-sparks-debate-20170630/

In any case, the discovery is based on a short segment of two continuous measurements having an approximately matching pattern (see the plot in the link above). My question is if this match could be just a random coincidence.

Consider two people continuously tossing coins in separate rooms. The results are recorded and correlated. At first they are seemingly random, but given time, there is a certain probability that the results would temporarily match. And the longer we observe, the more likely we get similar patterns.

I have observed a real roulette in a casino for the result to be red or black. Just on the second day of my observation the roulette produced 20 reds in a row. Superficially this is highly improbable, but so is the entire reality.

My question is, what is the margin of error in the gravitational waves discovery data from the standpoint of the probabilistic random coincidence that just looks like correlated signals?

Qmechanic
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safesphere
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    Since you're questioning about the discovery of gravitational waves, which is best understood by LIGO, I will recommend you that in addition to this question here, you may send your queries to questions@ligo.org. they will be able to help you in the best way. By the way, at LIGO, two detectors at Hanford and Livingston have simultaneously observed gravitational waves three times. The active and passive damping systems at LIGO cancel out any noise and result in a very very very efficient signal processing. – Wrichik Basu Aug 31 '17 at 15:46
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    I don't know the answer, but do consider that LIGO has people who are experts are calculating the probability that something is random chance. This possibility has occurred to them and they have confidence in their results, otherwise they wouldn't have published them. – Javier Aug 31 '17 at 15:47
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    IIRC the counter analysis of the linked arxiv paper has been challenged as the authors used an preliminary version of the software. – ZeroTheHero Aug 31 '17 at 16:03
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    In the science world, there is an effect: if somebody says, "X is bad, it was a mistake, because...", everybody hears it. If somebody says, "X is okay, we confirmed it on another way", it attracts much lesser attention. It surely won't get to the main page of popular sites. Don't forget this effect if you read physics news. – peterh Aug 31 '17 at 16:49
  • This is a good question but an historical insight (which doesn't actually address your question of whether this is a false positive): this dispute is exactly as has happenned with the coming of anything radically new in science. The disputes are, in the grand scheme of things, ultimately not very relevant, because the wrong party will in the end be quashed by empirical evidence. Given that the rate of detection is a few events per year, even if LIGO is premature, we won't have to wait too many years to sort this out. – Selene Routley Sep 01 '17 at 00:07
  • @WetSavannaAnimal: My question isn't if the discovery was a false positive. I'm not sure why most everyone here assumes this - must be their wishful thinking or perhaps my poor phrasing. My question is specifically what the margin of error was. I got the answer that it was 5.1 sigma according to the team, but questioned by others. Therefore the true margin of error is unknown. This answers my question as marked. – safesphere Sep 01 '17 at 03:23
  • No, I do understand that, and I'm guessing that most readers do. I think people are assuming the purpose of your question (which may be where we are in error), but the most obvious use for a margin of error / confidence level would be to gauge probability of an incorrect conclusion. It is a good question, because there are very few readable accounts of how these confidence levels are arrived at and what prior assumptions go into calculating them. – Selene Routley Sep 01 '17 at 04:06

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According the LIGO publication:

false alarm rate [is] estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than $5.1\sigma$.

With respect to being called into question, as of today (August 2017) there's still no agreement on that.

After the criticism by the Niels Bohr Institute (NBI) group; the answer from a member of the LIGO collaboration; and the reply from by NBI group; this August (2017) members of the LIGO collaboration visited the NBI for two weeks of discussions. It apparently became clear that there remain "in-principle disagreements" between the teams, with the NBI group summarizing their position on Aug 21st:

We believe that LIGO has not yet attained acceptable standards of data cleaning. Since we regard proof of suitable cleaning as a mandatory prerequisite for any meaningful comparison with specific astrophysical models of GW events, we continue to regard LIGO's claims of GW discovery as interesting but premature.

The community appeared to show a mostly skeptical reaction to the original NBI group paper, and it might be heading to obscurity. If so, it'll be hopefully reflecting flaws in the criticism $-$ and not an over-reliance on the authority of the LIGO collaboration.

stafusa
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    An historical answer: this dispute is exactly as has happenned with the coming of anything radically new in science. The disputes are, in the grand scheme of things, ultimately not very relevant, because the wrong party will in the end be quashed by empirical evidence. Given that the rate of detection is a few events per year, even if LIGO is premature, we won't have to wait too many years to sort this out. – Selene Routley Sep 01 '17 at 00:04
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    @WetSavannaAnimalakaRodVance That's my expectation too, especially due to the other detectors. My mood is a bit darker in my answer, I realize now. That's probably out of frustration for not finding myself competent enough to judge the issue myself. – stafusa Sep 01 '17 at 00:11
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    Yes, I think you won't be the only person disappointed if LIGO does turn out to be premature. But stats is incredibly subtle, probably the subtlest of human endeavors. Unless one belongs to of the teams living and breathing it, I don't think one can claim to be qualified at all to answer such questions alone. – Selene Routley Sep 01 '17 at 00:14
  • Since the question was about random coincidences, I think that the paper from the Niels Bohr Institute does not actually matter here too much: From what I unterstand from that paper, they claim to have found evidence for an intrinsic correlation of the data of the two detectors. As far as I can tell, they are not questioning the statistical significance of the event in the data, just its interpretation. (Coincidentally, I believe that their paper is critically missing an analysis of the statistical significance of their own findings, but that's a different story.) – Emil Sep 10 '17 at 10:20