A Markov Chain Monte Carlo Algorithm for Analysis of Low Signal-To-Noise Cosmic Microwave Background Data
Abstract
We present a new Markov Chain Monte Carlo (MCMC) algorithm for cosmic microwave background (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 ell, followed by a particular deterministic rescaling operation of the sky signal, s. The acceptance probability for this joint move depends on the sky map only through the difference of χ2 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.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- May 2009
- DOI:
- 10.1088/0004-637X/697/1/258
- arXiv:
- arXiv:0807.0624
- Bibcode:
- 2009ApJ...697..258J
- Keywords:
-
- cosmic microwave background;
- cosmology: observations;
- methods: numerical;
- Astrophysics;
- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- Submitted to ApJ