It seems to me that there are two key questions in thinking about the
Balazs et al result.
First, is their result truly "surprising"? That is, is their post-hoc
probability estimate 2e-6 valid? Post-hoc probability estimates -- and
their interpretation -- are always a bit dubious, because it's hard to
estimate how many other "equally surprising" patters there might be
which noone has thought to look for.
[If I flip a (fair) coin 10 times in a row, and it
comes up heads every time, that seems rather surprising.
But if you then learn that I'm an insomniac, and do a
dozen or so sets of 10-coin-flippings every night when
I can't sleep, then it's easy to see that I can expect
to get a 10-heads-in-a-row outcome every few months...
so getting one last night wasn't so surprising after all.
In other words, with frequentist statistics, to assess
an experiment we don't just have to know about the
experiment, we also have to know about all the other
things the authors tried that "didn't work"!
This is of course one of the main arguments for taking
a Bayesian perspective. Offhand I'm not sure what a
Bayesian analysis of the Balazs et al input catalog
would look like...]
Second, their result is based on finding 9 "ring" GRBs in a catalog
of 361 GRBs with known redshifts. Since more GRB redshifts are being
measured all the time, if there is truly a physical overdensity of
GRBs in the universe in the region of the sky found by Balazs et al,
then in a few years (when we'll have a much larger GRB-redshift catalog
available) the Balazs et al result should be confirmed in a much more
convincing manner.
And since Balazs et al have pointed to a specific sky region, if we
re-check that specific region with a new GRB-redshift catalog
[I.e., if we re-check using a catalog which does NOT
contain any of the 361 GRBs analysed by Balazs et al]
a few years from now, we won't suffer from the post-hoc-statistics
problem any more.
So, my reaction to Balazs et al is basically "wait and see". If the
result is genuine, within a few years we should have a confirmation
without post-hoc statistics. And if we don't get that confirmation,
that will imply that the result was basically a statistical fluke.
--
-- "Jonathan Thornburg [remove -animal to reply]" <
jth...@astro.indiana-zebra.edu>
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"There was of course no way of knowing whether you were being watched
at any given moment. How often, or on what system, the Thought Police
plugged in on any individual wire was guesswork. It was even conceivable
that they watched everybody all the time." -- George Orwell, "1984"