Forecasts of non-Gaussian parameter spaces using Box-Cox transformations
  Forecasts of statistical constraints on model parameters using the Fisher
matrix abound in many fields of astrophysics. The Fisher matrix formalism
involves the assumption of Gaussianity in parameter space and hence fails to
predict complex features of posterior probability distributions. Combining the
standard Fisher matrix with Box-Cox transformations, we propose a novel method
that accurately predicts arbitrary posterior shapes. The Box-Cox
transformations are applied to parameter space to render it approximately
multivariate Gaussian, performing the Fisher matrix calculation on the
transformed parameters. We demonstrate that, after the Box-Cox parameters have
been determined from an initial likelihood evaluation, the method correctly
predicts changes in the posterior when varying various parameters of the
experimental setup and the data analysis, with marginally higher computational
cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher
formalism to forecast cosmological parameter constraints by future weak
gravitational lensing surveys. The characteristic non-linear degeneracy between
matter density parameter and normalisation of matter density fluctuations is
reproduced for several cases, and the capabilities of breaking this degeneracy
by weak lensing three-point statistics is investigated. Possible applications
of Box-Cox transformations of posterior distributions are discussed, including
the prospects for performing statistical data analysis steps in the transformed
Gaussianised parameter space.
