Geometrical Aspects on Parameter estimation of stochastic gravitational
  wave background: beyond the Fisher analysis
  The maximum likelihood method is often used for parameter estimation in
gravitational wave astronomy. Recently, an interesting approach was proposed by
Vallisneri to evaluate the distributions of parameter estimation errors
expected for the method. This approach is to statistically analyze the local
peaks of the likelihood surface, and works efficiently even for signals with
low signal-to-noise ratios. Focusing special attention to geometric structure
of the likelihood surface, we follow the proposed approach and derive formulae
for a simplified model of data analysis where the target signal has only one
intrinsic parameter, along with its overall amplitude. Then we apply our
formulae to correlation analysis of stochastic gravitational wave background
with a power-law spectrum. We report qualitative trends of the formulae using
numerical results specifically obtained for correlation analysis with two
Advanced-LIGO detectors.
