Improving PSF modelling for weak gravitational lensing using new methods
  in model selection
  A simple theoretical framework for the description and interpretation of
spatially correlated modelling residuals is presented, and the resulting tools
are found to provide a useful aid to model selection in the context of weak
gravitational lensing. The description is focused upon the specific problem of
modelling the spatial variation of a telescope point spread function (PSF)
across the instrument field of view, a crucial stage in lensing data analysis,
but the technique may be used to rank competing models wherever data are
described empirically. As such it may, with further development, provide useful
extra information when used in combination with existing model selection
techniques such as the Akaike and Bayesian Information Criteria, or the
Bayesian evidence. Two independent diagnostic correlation functions are
described and the interpretation of these functions demonstrated using a
simulated PSF anisotropy field. The efficacy of these diagnostic functions as
an aid to the correct choice of empirical model is then demonstrated by
analyzing results for a suite of Monte Carlo simulations of random PSF fields
with varying degrees of spatial structure, and it is shown how the diagnostic
functions can be related to requirements for precision cosmic shear
measurement. The limitations of the technique, and opportunities for
improvements and applications to fields other than weak gravitational lensing,
are discussed.
