Comment on cluster analysis of radio loops in CMB data
  A recent article (Liu et al. 2014) looks for evidence in the WMAP internal
linear combination map (ILC) of unmodeled emission from the galactic radio loop
known as Loop I. The statistically strongest result comes from a cluster
analysis that tests whether the "hot spots" within a $20^\circ$ annulus at Loop
I are preferentially located near the center line of the annulus. From this
cluster analysis the authors report a $p$-value of 0.018% when considering the
four highest bins (75-87 $\mu$K). I show that the reported statistical
significance has been overestimated. First, the analysis does not correctly
select the hot spots in the simulated sky realizations; second, it is sensitive
to the map pixelization used, and in particular, pixel size used is similar to
the relevant clustering distance. I have run 10,000 simulated sky realizations
to reproduce the analysis in Liu et al. and to calculate the effects of
incorrect hot spot selection and of pixelization. Accounting for both of these
effects, I find a corrected $p$-value of $\sim1\%$, both in the highest-bin
test and in the four-bin test. Finally, I note that even under the assumption
that Loop I contributes significant power to the ILC map, the observed
clustering remains very unlikely. Therefore, a result inconsistent with
statistical isotropy is not automatically strong evidence for a detection of
Loop I. I suggest additional tests that could clarify the degree to which the
cluster analysis supports a detection of Loop I in the CMB map.
