BeyondPlanck IV. On end-to-end simulations in CMB analysis -- Bayesian versus frequentist statistics

Abstract

End-to-end simulations play a key role in the analysis of any high-sensitivity CMB experiment, providing high-fidelity systematic error propagation capabilities unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data, or as a random realization independent from the data. We refer to these as Bayesian and frequentist simulations, respectively. We show that the two options lead to significantly different correlation structures, as frequentist simulations, contrary to Bayesian simulations, effectively include cosmic variance, but exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties, and we argue that they therefore also have different and complementary scientific uses, even if this dichotomy is not absolute. Before BeyondPlanck, most pipelines have used a mix of constrained and random inputs, and used the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. BeyondPlanck represents the first end-to-end CMB simulation framework that is able to generate both types of simulations, and these new capabilities have brought this topic to the forefront. The Bayesian BeyondPlanck simulations and their uses are described extensively in a suite of companion papers. In this paper we consider one important applications of the corresponding frequentist simulations, namely code validation. That is, we generate a set of 1-year LFI 30 GHz frequentist simulations with known inputs, and use these to validate the core low-level BeyondPlanck algorithms; gain estimation, correlated noise estimation, and mapmaking.

References in corpus (22)

• Astropy: A Community Python Package for Astronomy
• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package
• Binary companions of evolved stars in APOGEE DR14: Search method and catalog of ~5,000 companions
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• Planck 2013 results. I. Overview of products and scientific results
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• Planck 2018 results. V. CMB power spectra and likelihoods
• Planck intermediate results. LVII. Joint Planck LFI and HFI data processing
• Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling
• Power spectrum estimation from high-resolution maps by Gibbs sampling
• Planck 2018 results. II. Low Frequency Instrument data processing
• BeyondPlanck III. Commander3
• BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data
• BeyondPlanck XIII. Intensity foreground sampling, degeneracies, and priors
• BeyondPlanck VII. Bayesian estimation of gain and absolute calibration for CMB experiments
• BeyondPlanck X. Bandpass and beam leakage corrections
• From BeyondPlanck to Cosmoglobe: Preliminary $WMAP$ $Q$-band analysis
• BeyondPlanck XI. Bayesian CMB analysis with sample-based end-to-end error propagation
• BeyondPlanck VI. Noise characterization and modelling
• BeyondPlanck X. Planck LFI frequency maps with sample-based error propagation
• BeyondPlanck II. CMB map-making through Gibbs sampling

Cited by in corpus (7)

• Cosmoglobe DR1 results. II. Constraints on isotropic cosmic birefringence from reprocessed WMAP and Planck LFI data
• BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data
• BeyondPlanck VII. Bayesian estimation of gain and absolute calibration for CMB experiments
• Cosmoglobe DR1 results. I. Improved Wilkinson Microwave Anisotropy Probe maps through Bayesian end-to-end analysis
• BeyondPlanck XII. Cosmological parameter constraints with end-to-end error propagation
• BeyondPlanck X. Planck LFI frequency maps with sample-based error propagation
• On the computational feasibility of Bayesian end-to-end analysis of LiteBIRD simulations within Cosmoglobe