An improved Markov-chain Monte Carlo sampler for the estimation of cosmological parameters from CMB data

Abstract

Markov-chain Monte Carlo sampling has become a standard technique for exploring the posterior distribution of cosmological parameters constrained by observations of CMB anisotropies. Given an infinite amount of time, any MCMC sampler will eventually converge such that its stationary distribution is the posterior of interest. In practice, however, naive samplers require a considerable amount of time to explore the posterior distribution fully. In the best case, this results only in wasted CPU time, but in the worse case can lead to underestimated confidence limits on the values of cosmological parameters. Even for the current CMB data set, the sampler employed in the widely-used cosmomc package does not sample very efficiently. This difficulty is yet more pronounced for data sets of the quality anticipated for the Planck mission. We thus propose a new MCMC sampler for analysing total intensity CMB observations, which can be easily incorporated into the cosmomc software, but has rapid convergence and produces reliable confidence limits. This is achieved by using dynamic widths for proposal distributions, dynamic covariance matrix sampling, and a dedicated proposal distribution for moving along well-known degeneracy directions.