Bayesian inference of CMB gravitational lensing
  The Planck satellite, along with several ground based telescopes, have mapped
the cosmic microwave background (CMB) at sufficient resolution and
signal-to-noise so as to allow a detection of the subtle distortions due to the
gravitational influence of the intervening matter distribution. A natural
modeling approach is to write a Bayesian hierarchical model for the lensed CMB
in terms of the unlensed CMB and the lensing potential. So far there has been
no feasible algorithm for inferring the posterior distribution of the lensing
potential from the lensed CMB map. We propose a solution that allows efficient
Markov Chain Monte Carlo sampling from the joint posterior of the lensing
potential and the unlensed CMB map using the Hamiltonian Monte Carlo technique.
The main conceptual step in the solution is a re-parameterization of CMB
lensing in terms of the lensed CMB and the "inverse lensing" potential. We
demonstrate a fast implementation on simulated data including noise and a sky
cut, that uses a further acceleration based on a very mild approximation of the
inverse lensing potential. We find that the resulting Markov Chain has short
correlation lengths and excellent convergence properties, making it promising
for application to high resolution CMB data sets of the future.
