Undergrad New measurement of the Hubble Parameter

[windy miller]

TL;DR

New measurement of Hubble Parameter from GW

I just saw a new paper on measuring the Hubble Parameter : https://arxiv.org/pdf/1908.06060.pdf
It seems they are agreeing with Planck which I understand would speak largely against the idea of new physics from the Hubble tension.
However it says +14 and -7 next to the estimate. I presume these are the error bars. Are they saying it could be as high as 82 or as low as 61? Is that right? in which case I guess this paper isn't very conclusive . Over the years as they get more measurement the error bars will come down and we'll see where the chips land. So we shouldn't get very excited by this result. Is that right?

 

[phyzguy]

Those look to be the one-sigma error bars. So it is saying there is 68% chance that H0 is between 61 and 82, a 95% chance that it is between 54 and 96, and a 99.7% chance that it is between 47 and 110. So, as you say, it is inconclusive and nothing to get excited about. Yes, as more GW events come in, the measurements will get better and the error bars will come down. However, this will take a long time, since it's going to take hundreds of events before the errors in these measurements get small enough to be able to weigh in on the current discrepancy.

 

[windy miller]

thanks

 

[Stephen Tashi]

The paper says it employs a method of Bayesian analysis explained by "Gray et al", but that reference is "TBD". Is there a standard method of Bayesian statistics used by cosmologists?

The thread https://www.physicsforums.com/threa...rpretation-and-credibility-confidence.975683/ asks for an interpretation of "prior" in a paper about cosmology. It would nice for someone to answer the question, but the paper it asks about ( https://arxiv.org/pdf/1709.10504.pdf ) doesn't explain the statistical methods it uses.

 

[kimbyd]

Those look to be the one-sigma error bars. So it is saying there is 68% chance that H0 is between 61 and 82, a 95% chance that it is between 54 and 96, and a 99.7% chance that it is between 47 and 110. So, as you say, it is inconclusive and nothing to get excited about. Yes, as more GW events come in, the measurements will get better and the error bars will come down. However, this will take a long time, since it's going to take hundreds of events before the errors in these measurements get small enough to be able to weigh in on the current discrepancy.

Extrapolating error bars like that doesn't really work that well, unfortunately. The asymmetry means that the errors are highly non-Gaussian, so applying Gaussian assumptions is doomed to fail.

Even with symmetric distributions, the real errors often get pretty far off once you get to the 3-sigma level, as most error distributions are pretty highly non-Gaussian. Typically, the real errors tend to be "fatter" than a Gaussian distribution, meaning that there's higher probability of large deviations from the mean than you'd expect. For instance, you might expend from a Gaussian distribution that values above 110 would occur with around 0.3% probability, given this experiment, but in reality the probability might be around 1%.

This is a big reason why theorists I knew back when I worked in physics basically took the view, "Let's just try to get the error bars so tight that there really isn't any doubt as to what's going on."