A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data

TL;DR

This paper introduces a new Monte Carlo Markov Chain algorithm that efficiently analyzes low signal-to-noise CMB data by combining Metropolis-Hastings and Gibbs sampling techniques, improving upon previous methods.

Contribution

The paper presents a novel MCMC algorithm that effectively addresses low signal-to-noise challenges in CMB data analysis, enhancing computational efficiency over existing Gibbs samplers.

Findings

Efficient joint sampling of CMB power spectrum and sky signal.

High acceptance rate in low signal-to-noise regime.

Applicable to both high and low signal-to-noise data.

Abstract

We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C_l, followed by a particular deterministic rescaling operation of the sky signal. The acceptance probability for this joint move depends on the sky map only through the difference of chi-squared between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.