Almanac: MCMC-based signal extraction of power spectra and maps on the sphere

TL;DR

Almanac employs Hamiltonian Monte Carlo to infer detailed, high-dimensional cosmological maps and power spectra from noisy celestial data, providing robust, model-independent posterior distributions and handling complex signal-to-noise variations.

Contribution

It introduces a novel MCMC-based method for joint inference of all-sky maps and power spectra, including $E$- and $B$-modes, avoiding leakage issues and enabling detailed posterior analysis.

Findings

Successfully infers $E$- and $B$-mode power spectra from simulated data.

Handles millions of parameters with variable signal-to-noise ratios.

Provides science-ready posterior data products for cosmological analysis.

Abstract

Inference in cosmology often starts with noisy observations of random fields on the celestial sphere, such as maps of the microwave background radiation, continuous maps of cosmic structure in different wavelengths, or maps of point tracers of the cosmological fields. Almanac uses Hamiltonian Monte Carlo sampling to infer the underlying all-sky noiseless maps of cosmic structures, in multiple redshift bins, together with their auto- and cross-power spectra. It can sample many millions of parameters, handling the highly variable signal-to-noise of typical cosmological signals, and it provides science-ready posterior data products. In the case of spin-weight 2 fields, Almanac infers $E$- and $B$-mode power spectra and parity-violating $EB$ power, and, by sampling the full posteriors rather than point estimates, it avoids the problem of $EB$-leakage. For theories with no $B$-mode signal, inferred non-zero $B$-mode power may be a useful diagnostic of systematic errors or an indication of new physics. Almanac's aim is to characterise the statistical properties of the maps, with outputs that are completely independent of the cosmological model, beyond an assumption of statistical isotropy. Inference of parameters of any particular cosmological model follows in a separate analysis stage. We demonstrate our signal extraction on a CMB-like experiment.