Fast optimal CMB power spectrum estimation with Hamiltonian sampling

TL;DR

This paper introduces a fast, flexible Hamiltonian Monte Carlo method for optimal estimation of the cosmic microwave background temperature power spectrum, outperforming traditional approaches especially in low signal-to-noise regimes.

Contribution

It presents a novel application of Hamiltonian Monte Carlo sampling for efficient, high-resolution CMB power spectrum estimation, demonstrating advantages over Gibbs sampling.

Findings

HMC performs favorably compared to Gibbs sampling in low S/N regimes.

Analysis of WMAP-sized data sets is feasible in around eighty hours.

The method is flexible and imposes few conditions on the distribution to be sampled.

Abstract

We present a method for fast optimal estimation of the temperature angular power spectrum from observations of the cosmic microwave background. We employ a Hamiltonian Monte Carlo (HMC) sampler to obtain samples from the posterior probability distribution of all the power spectrum coefficients given a set of observations. We compare the properties of the HMC and the related Gibbs sampling approach on low-resolution simulations and find that the HMC method performs favourably even in the regime of relatively low signal-to-noise. We also demonstrate the method on high-resolution data by applying it to simulated WMAP data. Analysis of a WMAP-sized data set is possible in a around eighty hours on a high-end desktop computer. HMC imposes few conditions on the distribution to be sampled and provides us with an extremely flexible approach upon which to build.