Bayesian inference of CMB gravitational lensing

TL;DR

This paper introduces a Bayesian hierarchical model and an efficient Hamiltonian Monte Carlo algorithm for jointly inferring the CMB lensing potential and the unlensed CMB map, enabling improved analysis of high-resolution CMB data.

Contribution

It presents a novel re-parameterization and a fast MCMC sampling method for Bayesian inference of CMB lensing, addressing previous computational challenges.

Findings

Efficient MCMC sampling with short correlation lengths.

Good convergence properties demonstrated on simulated data.

Potential for application to future high-resolution CMB datasets.

Abstract

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.