BeyondPlanck II. CMB map-making through Gibbs sampling

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.

11 pages, 10 figures. All BeyondPlanck products and software will be released publicly at http://beyondplanck.science during the online release conference (November 18-20, 2020). Connection details will be made available at the same website. Registration is mandatory for the online tutorial, but optional for the conference

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• Making sky maps from Planck data
• BeyondPlanck III. Commander3
• Making Maps from Planck LFI 30GHz Data
• Map-making in small field modulated CMB polarisation experiments: approximating the maximum-likelihood method
• BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data
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Cited by in corpus (4)

• BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data
• BeyondPlanck VI. Noise characterization and modelling
• BeyondPlanck IV. On end-to-end simulations in CMB analysis -- Bayesian versus frequentist statistics
• Systematic effects on lensing reconstruction from a patchwork of CMB polarization maps