Fast, exact CMB power spectrum estimation for a certain class of observational strategies

Abstract

We describe a class of observational strategies for probing the anisotropies in the cosmic microwave background (CMB) where the instrument scans on rings which can be combined into an n-torus, the {\em ring torus}. This class has the remarkable property that it allows exact maximum likelihood power spectrum estimation in of order $N^2$ operations (if the size of the data set is $N$) under circumstances which would previously have made this analysis intractable: correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes, non-uniform distribution of integration time on the sky and partial sky coverage. This ease of computation gives us an important theoretical tool for understanding the impact of instrumental effects on CMB observables and hence for the design and analysis of the CMB observations of the future. There are members of this class which closely approximate the MAP and Planck satellite missions. We present a numerical example where we apply our ring torus methods to a simulated data set from a CMB mission covering a 20 degree patch on the sky to compute the maximum likelihood estimate of the power spectrum $C_{\ell }$ with unprecedented efficiency.

RevTeX, 14 pages, 5 figures. A full resolution version of Figure 1 and additional materials are at http://feynman.princeton.edu/~bwandelt/RTM

References in corpus (1)

• CMB Power Spectrum Estimation via Hierarchical Decomposition

Cited by in corpus (33)

• Fast and scalable Gaussian process modeling with applications to astronomical time series
• A unified pseudo-$C_{\ell }$ framework
• CMB-S4 Science Book, First Edition
• Fast estimation of polarization power spectra using correlation functions
• Myths and Truths Concerning Estimation of Power Spectra
• Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling
• Power spectrum estimation from high-resolution maps by Gibbs sampling
• Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background
• Algorithms for bispectra: forecasting, optimal analysis, and simulation
• Bayesian Power Spectrum Analysis of the First-Year WMAP data
• Unbiased Estimation of an Angular Power Spectrum
• Fast optimal CMB power spectrum estimation with Hamiltonian sampling
• Disconnected pseudo-$C_{\ell }$ covariances for projected large-scale structure data
• Fast CMB Power Spectrum Estimation of Temperature and Polarisation with Gabor Transforms
• Cross-Correlation of Planck CMB Lensing with DESI-Like LRGs
• CMB power spectrum estimation using noncircular beams
• Searching for quasi-periodic oscillations in astrophysical transients using Gaussian processes
• Cosmic microwave background power spectrum estimation with the destriping technique
• The effects of low temporal frequency modes on minimum variance maps from PLANCK
• Asymfast, a method for convolving maps with asymmetric main beams
• Data analysis methods for the cosmic microwave background
• Likelihood, Fisher information, and systematics of cosmic microwave background experiments
• Effects of Destriping Errors on CMB Polarisation Power Spectra and and Pixel Noise Covariances
• Fast calculation of the Fisher matrix for cosmic microwave background experiments
• Power spectrum sensitivity of raster-scanned CMB experiments in the presence of 1/f noise
• CMB power spectrum estimation with non-circular beam and incomplete sky coverage
• Accelerating Cosmic Microwave Background map-making procedure through preconditioning
• Non-Circular beam correction to the CMB power spectrum
• Estimation of Full Sky Power Spectrum between Intermediate to Large Angular Scales from Partial Sky CMB Anisotropies using Artificial Neural Network
• An Unbiased Estimator of the Full-sky CMB Angular Power Spectrum at Large Scales using Neural Networks
• Gaussian Process Modelling for Improved Resolution in Faraday Depth Reconstruction
• PoPE: A population-based approach to model spatial structure of astronomical systems
• Cosmological Parameter Estimation: Method