BeyondPlanck II. CMB map-making through Gibbs sampling

TL;DR

This paper introduces a Gibbs sampling method for CMB map-making that improves computational efficiency and error analysis, enabling more accurate and systematic handling of noise and data gaps in Planck data simulations.

Contribution

It presents a novel Gibbs sampling approach for CMB map-making that separates noise filtering and map binning, allowing for efficient computation and better error characterization.

Findings

Gibbs sampling efficiently handles data gaps by noise filling.

The method produces a chain of map samples for posterior analysis.

Traditional solvers are faster for single maximum-likelihood maps.

Abstract

We present a Gibbs sampling solution to the map-making problem for CMB measurements, building on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps; noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods, and allows us for the first time to bring the destriping baseline length to a single sample. We apply the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we may compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction, and this methodology forms the conceptual basis for the map-making algorithm employed in the BeyondPlanck framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.