Improved Discussion of Vitale+

[farr]

Regarding the above publications, while they are cited and briefly discussed in the manuscript, their their presentation is somewhat lacking. Mainly, the result of Vitale et al. is said to carry out a similar analysis, but concludes that several hundred sources would be needed (see lines 166-169). In reality, Vitale et al. focuses on measuring the precise contributions of different channels, e.g. 70% vs. 20%, as opposed to ruling out the extreme cases in which all binaries originate from the same channel (as is considered in the present paper). The several hundred measurements will be needed for such precision measurements, not for ruling out extreme cases.

[farr]

Note that Salvo also writes (in LIGO P&P comments):

I am a bit concerned about the discussion of my paper, and in particular the idea that might be conveyed, that I got different results because I did something wrong.

In reality, I think the difference might be explained by the fact that my approach was a bit more general, since it assumed that either channels are followed. By contrast, if I understand properly (~line 100), you are assuming that all signals come from the same channel, and you focus on the odds between that channel and the others.

Thus, my ~100 events for ~10% uncertainty refers to a situation where both channels happen, and one measures the branching ratio.

I also considered a situation similar to what you have, Fig 2, where all signals come from the same channel, and there you say that after a few events the odds are already in favor of the right model at >3 sigma (black line) level for most catalogs (and after ~20 events for all catalogs). I think that plot represents a fairer comparison with your results.

Another important factor, is that your test is based on chi_eff, while my test was based on individual spins, which are estimated less well.