Optimisation of the Population Monte Carlo algorithm: Application to constraining isocurvature models with cosmic microwave background data
Abstract
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 Ddimensional 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 nineyear 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 that the number of sample points increase by factors of 3 and 20, respectively, relative: to the optimal Gaussian case. This is due to degeneracies in the underlying parameter space. The WMAP nineyear data constrain the admixture model to have an isocurvature fraction of 36.3 ± 2.8%.
 Publication:

Astronomische Nachrichten
 Pub Date:
 June 2016
 DOI:
 10.1002/asna.201512359
 arXiv:
 arXiv:1510.01486
 Bibcode:
 2016AN....337..672M
 Keywords:

 cosmic microwave background;
 cosmological parameters;
 methods: numerical;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 21 pages, 10 figures