Cosmological Parameters from CMB Maps without Likelihood Approximation
  We propose an efficient Bayesian MCMC algorithm for estimating cosmological
parameters from CMB data without use of likelihood approximations. It builds on
a previously developed Gibbs sampling framework that allows for exploration of
the joint CMB sky signal and power spectrum posterior, P(s,Cl|d), and addresses
a long-standing problem of efficient parameter estimation simultaneously in
high and low signal-to-noise regimes. To achieve this, our new algorithm
introduces a joint Markov Chain move in which both the signal map and power
spectrum are synchronously modified, by rescaling the map according to the
proposed power spectrum before evaluating the Metropolis-Hastings accept
probability. Such a move was already introduced by Jewell et al. (2009), who
used it to explore low signal-to-noise posteriors. However, they also found
that 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 filter
mean field from the proposed map prior to rescaling, leaving high
signal-to-noise information invariant in the joint step, and effectively only
rescaling the low signal-to-noise component. To explore the full posterior, the
new joint move is then interleaved with a standard conditional Gibbs sky map
move. We apply our new algorithm to simplified simulations for which we can
evaluate the exact posterior to study both its accuracy and performance, and
find good agreement with the exact posterior; marginal means agree to less than
0.006 sigma, and standard deviations to better than 3%. The Markov Chain
correlation length is of the same order of magnitude as those obtained by other
standard samplers in the field.
