Re: [IPTA-cs] Bayesian upper limits

[Ken Olum <kdo cosmos phy tufts edu>]

Is the suggestion really that upper limits should depend on a prior for
the quantity being limited?  This seems rather scary, and also not what
I would want.  Suppose I come up with some particle physics theory in
which there should be strings with some G mu.  I wonder whether this
possibility is already ruled out.  I would like to look at a paper and
see whether observations are strongly at odds with this G mu.  This
shouldn't depend on what the authors of that paper used as a prior for G
mu.  I don't care anything about other possible G mu; I just want to
find out what observations have to say about my suggestion.

I don't mind the upper limit on G mu depending on the prior for other
quantities, such as A_GWB.  That seems to make sense: If the data is
well explained by a GWB, then introducing strings will make the fit
worse.  But if the requisite GWB amplitude is disfavored by a prior, then
strings look better.  On the other hand, one would hope that there is
not a very large dependence on this prior.

I find any use of uniform priors pretty scary.  Suppose I put a uniform
prior on G mu from 0 to 10^-6.  That means that 99.9% of the time, G mu >
10^-9.  Such signals are clearly incompatible with observations.  So,
using this prior, I would conclude that cosmic strings are ruled out at
the 99.9% level.  But that's not the right conclusion.  Actually the data
say nothing about G mu = 10^-12.  This low value was ruled out by the
prior; it would be wrong to say that it was ruled out by observation.

                                        Ken