How does the tensor-to-scalar ratio depend on the prior adopted? A reviewer for one of my papers made the comment that the "tensor-to-scalar ratio is sensitive to the prior adopted" and asks if I'm able to work out the prior using the methods in the paper.
I don't understand what the reviewer means. As I understand the tensor-to-scalar ratio, it's a measured quantity, in which case it shouldn't have a prior. Does anyone know what the reviewer is referring to? I realize I can ask the reviewer for clarification, but it's a bit time-consuming.
 A: I'm just guessing what the reviewer might have meant. In cosmology, statistical analysis is done with Bayesian inference. In that case the measured value of any parameter is some description of the posterior distribution for that parameter (like a median value and 90% credible interval). The posterior is a combination of the likelihood and prior. So any measurement is prior-dependent. In the limit where you have a large signal-to-noise ratio, the prior shouldn't matter too much. But in the case of the tensor-to-scalar ratio, where there is only an upper limit, the prior does play a role in determining the value of the upper limit. For example, you generally will get a smaller upper limit if you assume a prior that is uniform in the log of the parameter, instead of uniform in the parameter. If you are using a value of the tensor-to-scalar ratio based on an upper limit coming from a Bayesian analysis, the reviewer may be asking you to clarify what prior was used to obtain that upper limit.
If you did the analysis yourself, you should know the prior. If you got the measured value (upper limit) from a paper, they should say what prior they used in the paper. If they didn't, that's a reason to be suspicious.
