Detecting anomalies in CMB maps: a new method

Ever since WMAP announced its first results, different analyses have shown that there is weak evidence for several large-scale anomalies in the CMB data. While the evidence for each anomaly appears to be weak, the fact that there are multiple seemingly unrelated anomalies makes it difficult to account for them via a single statistical fluke. So, one is led to considering a combination of these anomalies. But, if we "hand-pick" the anomalies (test statistics) to consider, we are making an \textit{a posteriori} choice. In this article, we propose two statistics that do not suffer from this problem. The statistics are linear and quadratic combinations of the $a_{\ell m}$'s with random co-efficients, and they test the null hypothesis that the $a_{\ell m}$'s are independent, normally-distributed, zero-mean random variables with an $m$-independent variance. The motivation for such statistics is generality; equivalently, it is a non \textit{a posteriori} choice. But, a very useful by-product of considering such statistics is this: Because most physical models that lead to large-scale anomalies result in coupling multiple $\ell$ and $m$ modes, the "coherence" of this coupling should get enhanced if a combination of different modes is considered. Using fiducial data, we demonstrate that the method works and discuss how it can be used with actual CMB data to make quite general statements about how incompatible the data are with the null hypothesis.