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.