A self-contained guide to the CMB Gibbs sampler

TL;DR

This paper provides a comprehensive, pedagogical review of the CMB Gibbs sampler, introduces a new C++ implementation called SLAVE, and discusses its applications in cosmological data analysis including foreground removal and power spectrum estimation.

Contribution

It introduces SLAVE, a new self-contained CMB Gibbs sampler in C++, and details its design, implementation, and applications in cosmological data analysis.

Findings

SLAVE is a functional, user-friendly CMB Gibbs sampler.

Demonstrated the algorithm for white noise level estimation.

Provided utilities for power spectrum estimation using Blackwell-Rao.

Abstract

We present a consistent self-contained and pedagogical review of the CMB Gibbs sampler, focusing on computational methods and code design. We provide an easy-to-use CMB Gibbs sampler named SLAVE developed in C++ using object-oriented design. While discussing why the need for a Gibbs sampler is evident and what the Gibbs sampler can be used for in a cosmological context, we review in detail the analytical expressions for the conditional probability densities and discuss the problems of galactic foreground removal and anisotropic noise. Having demonstrated that SLAVE is a working, usable CMB Gibbs sampler, we present the algorithm for white noise level estimation. We then give a short guide on operating SLAVE before introducing the post-processing utilities for obtaining the best-fit power spectrum using the Blackwell-Rao estimator.