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Re: [IPTA-cs] VOS versus BOS



Hi Ken (+All),

I guess we could do a similar comparison for our project once we have built up enough confidence in our code. As you were saying, at that stage, when the code has been debugged and is successfully running, it will be easy to look at several different model predictions simultaneously.

Given that you found a 0.4 sigma difference between the BOS and cusps-only points (for G\mu = 10^-10), I expect that, in our analysis, we should also find slightly different G\mu posterior histograms for your and my data sets, after all. On the other hand, I would say it remains to be seen whether we will be able to make any meaningful statements based on this variability in the G\mu posterior.

As we already known from Table 1 in your paper https://arxiv.org/abs/2102.08194 both posteriors should extend over a very similar range on the G\mu axis. (In your paper, the upper and lower bounds on G\mu for the "BOS" and "cusps" models only differ from each other in the third significant digit.) Plus, each posterior comes with an intrinsic variability if our chains have not yet fully converged. Therefore, before we can talk about differences between G\mu posteriors, we need to make sure that we reach the necessary precision for each individual posterior, which may be challenging.

Best regards, Kai.

On 6/16/22 18:52, Ken Olum via IPTA-cosmic-strings wrote:
Hi, Kai.  Thanks for straightening this out.  I agree that everything is
consistent now.  I don't know how much detail to go into in our paper.
This small difference in amplitudes (and also in spectral index, which
is basically the slope of the curves in your plot) can make some
difference in the fit to the data.  For example there's a difference on
the order of 0.4 sigma in the fit to the NANOGrav 12.5 year data between
the BOS point with Gmu = 10^-10 and the cusp-only point in
https://arxiv.org/abs/2102.08194.  It matters less for the Gmu that
are closer to the middle of the preferred range.

                                         Ken