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We propose an efficient Bayesian MCMC algorithm for estimating cosmologicalparameters from CMB data without use of likelihood approximations. It builds ona previously developed Gibbs sampling framework that allows for exploration ofthe joint CMB sky signal and power spectrum posterior, P(s,Cl|d), and addressesa long-standing problem of efficient parameter estimation simultaneously inhigh and low signal-to-noise regimes. To achieve this, our new algorithmintroduces a joint Markov Chain move in which both the signal map and powerspectrum are synchronously modified, by rescaling the map according to theproposed power spectrum before evaluating the Metropolis-Hastings acceptprobability. Such a move was already introduced by Jewell et al. (2009), whoused it to explore low signal-to-noise posteriors. However, they also foundthat the same algorithm is inefficient in the high signal-to-noise regime,since a brute-force rescaling operation does not account for phase information.This problem is mitigated in the new algorithm by subtracting the Wiener filtermean field from the proposed map prior to rescaling, leaving highsignal-to-noise information invariant in the joint step, and effectively onlyrescaling the low signal-to-noise component. To explore the full posterior, thenew joint move is then interleaved with a standard conditional Gibbs sky mapmove. We apply our new algorithm to simplified simulations for which we canevaluate the exact posterior to study both its accuracy and performance, andfind good agreement with the exact posterior; marginal means agree to less than0.006 sigma, and standard deviations to better than 3%. The Markov Chaincorrelation length is of the same order of magnitude as those obtained by otherstandard samplers in the field.

Cosmological Parameters from CMB Maps without Likelihood Approximation