Bayesian inference of CMB gravitational lensing

Understand

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.