Cosmic Shear E/B-mode Estimation with Binned Correlation Function Data
  In this work I study the problem of E/B-mode separation with binned cosmic
shear two-point correlation function data. Motivated by previous work on
E/B-mode separation with shear two-point correlation functions and the
practical considerations of data analysis, I consider E/B-mode estimators which
are linear combinations of the binned shear correlation function data points. I
demonstrate that these estimators mix E- and B-modes generally. I then show how
to define estimators which minimize this E/B-mode mixing and give practical
recipes for their construction and use. Using these optimal estimators, I
demonstrate that the vector space composed of the binned shear correlation
function data points can be decomposed into approximately ambiguous, E- and
B-mode subspaces. With simple Fisher information estimates, I show that a
non-trivial amount of information on typical cosmological parameters is
contained in the ambiguous mode subspace computed in this formalism. Next, I
give two examples which apply these practical estimators and recipes to generic
problems in cosmic shear data analysis: data compression and spatially locating
B-mode contamination. In particular, by using wavelet-like estimators with the
shear correlation functions directly, one can pinpoint B-mode contamination to
specific angular scales and extract information on its shape. Finally, I
discuss how these estimators can be used as part of blinded or closed-box
cosmic shear data analyses in order to assess and find B-mode contamination at
high-precision while avoiding observer biases.
