  In the past decade, weak gravitational lensing has become an important tool
in the study of the universe at the largest scale, giving insights into the
distribution of dark matter, the expansion of the universe, and the nature of
dark energy. This thesis research explores several applications of
Karhunen-Loeve (KL) analysis to speed and improve the comparison of weak
lensing shear catalogs to theory in order to constrain cosmological parameters
in current and future lensing surveys. After providing a brief introduction to
cosmology and to KL analysis, this work addresses three related aspects of weak
lensing analysis: (1) Three-dimensional tomographic mapping (based on work
published in Vanderplas et al. 2011); (2) Shear peak statistics with
incomplete/gappy data (based on work published in Vanderplas et al. 2012); and
(3) two-point parameter estimation from gappy data using KL modes (previously
unpublished)... [this abstract has been abbreviated; please see the thesis for
the full abstract].
