[1003.3451] Primordial Non-Gaussianity and the NRAO VLA Sky
Posted: March 19 2010
This paper claims to find ~3 sigma evidence for local-form non-Gaussianity
based on a measurement that the NVSS correlation function does not go to zero
by separations ~8 degrees, when it should have been consistent with zero by
~2-3 degrees for standard Gaussian LCDM (given their error bars).
My first question when seeing any correlation function that "does not go to
zero" is "doesn't any measured correlation function *need* to become
consistent with zero as you go to large separations, and why haven't the
authors shown me that theirs does??" In other words: you may or may not have
built in an integral constraint that forces your points to go negative
somewhere, but in any case you should have a term in the covariance
matrix corresponding to adding a constant to the correlation function, which
guarantees that any fit results will not be sensitive to a shift in the mean
of the survey (or scales much larger than the ones you think you can control).
It looks to me like the authors' measurement is essentially completely based on
this kind of constant term in the correlation function, i.e., if I am allowed
to add a constant to the Gaussian case, it doesn't look like it can be
distinguished from the non-Gaussian case. If the authors have some reason to
believe this is not a problem, it should be clarified in the paper.
That is a general observational consideration (you can't measure fluctuations
in the mean of your survey), but there is a related theoretical issue:
Naively, the constant contribution to the correlation function is
infinite in this model for non-Gaussianity (although they may be
leaving out the part of the calculation that gives that), so it is not clear
what their predictions that look like they are going flat at large separations
mean. There is an easy solution to both problems: marginalize over a free
constant added to the correlation function prediction. It seems pretty clear
though that they will find nothing of any significance when doing this.
This is really a general problem with the correlation function. Looking at it
at a given separation does not really correspond to what one is intuitively
thinking when thinking about a certain "scale", e.g., the value at a relatively
small separation is affected by fluctuations in something as large-scaled as
the mean of the survey. Usually this doesn't matter, however, because one has
measurements showing that the correlation goes to zero on scales larger than
the ones of interest (to better precision than the changes of interest on
your scale), which implicitly constrain the kind of constant term you should
generally marginalize over.
based on a measurement that the NVSS correlation function does not go to zero
by separations ~8 degrees, when it should have been consistent with zero by
~2-3 degrees for standard Gaussian LCDM (given their error bars).
My first question when seeing any correlation function that "does not go to
zero" is "doesn't any measured correlation function *need* to become
consistent with zero as you go to large separations, and why haven't the
authors shown me that theirs does??" In other words: you may or may not have
built in an integral constraint that forces your points to go negative
somewhere, but in any case you should have a term in the covariance
matrix corresponding to adding a constant to the correlation function, which
guarantees that any fit results will not be sensitive to a shift in the mean
of the survey (or scales much larger than the ones you think you can control).
It looks to me like the authors' measurement is essentially completely based on
this kind of constant term in the correlation function, i.e., if I am allowed
to add a constant to the Gaussian case, it doesn't look like it can be
distinguished from the non-Gaussian case. If the authors have some reason to
believe this is not a problem, it should be clarified in the paper.
That is a general observational consideration (you can't measure fluctuations
in the mean of your survey), but there is a related theoretical issue:
Naively, the constant contribution to the correlation function is
infinite in this model for non-Gaussianity (although they may be
leaving out the part of the calculation that gives that), so it is not clear
what their predictions that look like they are going flat at large separations
mean. There is an easy solution to both problems: marginalize over a free
constant added to the correlation function prediction. It seems pretty clear
though that they will find nothing of any significance when doing this.
This is really a general problem with the correlation function. Looking at it
at a given separation does not really correspond to what one is intuitively
thinking when thinking about a certain "scale", e.g., the value at a relatively
small separation is affected by fluctuations in something as large-scaled as
the mean of the survey. Usually this doesn't matter, however, because one has
measurements showing that the correlation goes to zero on scales larger than
the ones of interest (to better precision than the changes of interest on
your scale), which implicitly constrain the kind of constant term you should
generally marginalize over.