0
$\begingroup$

I've read:

To investigate the impact of reducing the parameter space for GRB searches, we will deliberately avoid the question of first gravitational wave detection - where a "5-sigma" observation may well be required (Abadie et al. 2012c). Instead, we consider a later observation for which we might require a specific false positive rate: i.e. a limit on the fraction gravitational wave observations are spurious. In that case, the threshold for announcing a detection is tied to the true signal rate.
[...]
When the advanced LIGO and Virgo detectors are operating at design sensitivity, the expected rate of observed BNS mergers is 20 per year. Thus the threshold corresponds to a false positive rate of 1 in 2000.

http://arxiv.org/abs/1409.8149

My understanding is that where $$ FAR=\text{False Alarm Rate}\\ FAP=\text{False Alarm Probability}\\ TSR=\text{True Signal Rate}\\ FPR=\text{False Positive Rate}\\ t=\text{Search Time} $$

R code:

FAR=1/100 #yr^-1 
TSR=20 #yr^-1
t=16/365 #yr

FAP=1-exp(-FAR*t)
Nsigma=qnorm(1-FAP)
FPR=FAR/(FAR+TSR)

Results:

> FAP
[1] 0.0004382601
> Nsigma
[1] 3.327427
> FPR
[1] 0.0004997501
> 1/FPR
[1] 2001

So it appears the plan is to lower the FAR threshold to $1/100~yr^{-1}$, which would correspond to a $3.3\sigma$ observation. To get a threshold of $5\sigma$, just change to $FAR=\frac{1}{200,000}~yr^{-1}$. This assumes a typical search time of $\frac{16}{365}~yr$, which was the case for GW150914. We could instead consider a longer search time of $1~yr$ or shorter of $\frac{1}{365}~yr$, which would correspond to $2.3\sigma$ and $4.0\sigma$ observations, respectively.

Is this really the plan? If so, what is the reasoning here? I can (somewhat) understand not bothering to report the estimated false positive rate when the TSR is extremely uncertain, but not why the threshold for detection should also become more lenient.

$\endgroup$
  • 2
    $\begingroup$ The cited paper seems to be discussing a particular search event: finding GRBs (gamma ray bursters) via gravitational waves. The LIGO news release says that the recent detection was 5.1 sigma. $\endgroup$ – Peter Diehr Feb 24 '16 at 20:05
  • $\begingroup$ @PeterDiehr I agree the focus of the paper is on a different type of event than GW150914, the calculation is also for neutron stars rather than black holes. However, there is nothing in the calculation referring to GrBs, and I've seen this threshold used elsewhere as well. For example, when estimating detector sensitivity the same is used: "We impose a nominal one-per-century threshold on the FAR". Anyway, the answer may very well be "No, that is not the plan". $\endgroup$ – Livid Feb 24 '16 at 20:27
  • 1
    $\begingroup$ GW150914 was, as far as I can tell, far larger than a $5\sigma$ event. This is about the gamma and x-ray signal detection being the primary signal that triggers an after-the-fact search for a very weak gravitational signal that normally wouldn't even make the LIGO cuts. The opposite scenario, which they are not interested in is that LIGO may find a gravitational signal that then triggers a search for the gamma signals. I am not sure that's even possible. The satellites are usually not equipped to store data that doesn't pass the triggers. That data is simply lost in space. $\endgroup$ – CuriousOne Feb 24 '16 at 20:28
  • $\begingroup$ @CuriousOne Thanks, that would make sense. So this calculation is just an example of what would make them look closer at a signal rather than "the threshold for announcing a detection". Regarding the latter, I don't think the actual sigma-level for a given event is relevant to error rates, since any signal passing the threshold would be announced. $\endgroup$ – Livid Feb 24 '16 at 20:53
  • $\begingroup$ The idea is that you take a clean trigger from the gamma satellites and then use that to search for a gravitational signal that is too weak to make the cut all by itself. It's a combined analysis with complicated biases, so I don't think a simple Gaussian analysis comes even close to getting the correct results for the significance and false detection rate. I am always skeptical when detector data is being analyzed "the easy" way. It's a little bit like armchair coaching... $\endgroup$ – CuriousOne Feb 24 '16 at 21:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.