Optimisation of the Population Monte Carlo algorithm: Application to
  constraining isocurvature models with cosmic microwave background data
  We optimise the parameters of the Population Monte Carlo algorithm using
numerical simulations. The optimisation is based on an efficiency statistic
related to the number of samples evaluated prior to convergence, and is applied
to a D-dimensional Gaussian distribution to derive optimal scaling laws for the
algorithm parameters. More complex distributions such as the banana and bimodal
distributions are also studied. We apply these results to a cosmological
parameter estimation problem that uses CMB anisotropy data from the WMAP
nine-year release to constrain a six parameter adiabatic model and a fifteen
parameter admixture model, consisting of correlated adiabatic and isocurvature
perturbations. In the case of the adiabatic model and the admixture model we
find respective degradation factors of three and twenty, relative to the
optimal Gaussian case, due to degeneracies in the underlying parameter space.
The WMAP nine-year data constrain the admixture model to have an isocurvature
fraction of at most $36.3 \pm 2.8$ percent.
