Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Scalar Edition
arXiv:2303.08828 · doi:10.1103/PhysRevD.107.123516
Abstract
We derive optimal estimators for the two-, three-, and four-point correlators of statistically isotropic scalar fields defined on the sphere, such as the Cosmic Microwave Background temperature fluctuations, allowing for arbitrary (linear) masking and inpainting schemes. In each case, we give the optimal unwindowed estimator (obtained via a maximum-likelihood prescription, with an associated Fisher deconvolution matrix), and an idealized form, and pay close attention to their efficient computation. For the trispectrum, we include both parity-even and parity-odd contributions, as allowed by symmetry. The estimators can include arbitrary weighting of the data (and remain unbiased), but are shown to be optimal in the limit of inverse-covariance weighting and Gaussian statistics. The normalization of the estimators is computed via Monte Carlo methods, with the rate-limiting steps (involving spherical harmonic transforms) scaling linearly with the number of bins. An accompanying code package, PolyBin, implements these estimators in Python, and we demonstrate the estimators' efficacy via a suite of validation tests.
arXiv comment33 pages, 10 figures, code available at https://github.com/oliverphilcox/PolyBin. Accepted by Phys. Rev. D
References in corpus (41)
- HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
- Planck 2018 results. X. Constraints on inflation
- Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
- MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
- Estimating the Power Spectrum of the Cosmic Microwave Background
- How to measure CMB power spectra without losing information
- Measuring primordial non-Gaussianity in the cosmic microwave background
- Measuring the galaxy power spectrum with future redshift surveys
- The shape of primordial non-Gaussianity and the CMB bispectrum
- An Efficient Technique to Determine the Power Spectrum from Cosmic Microwave Background Sky Maps
- CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation
- Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps
- Estimating non-gaussianity in the microwave background
- Probing Parity-Violation with the Four-Point Correlation Function of BOSS Galaxies
- Algorithms for bispectra: forecasting, optimal analysis, and simulation
- General CMB and Primordial Trispectrum Estimation
- The CMB Bispectrum
- A New Approach to Probing Primordial Non-Gaussianity
- Decorrelating the Power Spectrum of Galaxies
- Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background II: Partial Sky Coverage and Inhomogeneous Noise
- Cosmology Without Windows: Quadratic Estimators for the Galaxy Power Spectrum
- Colliding Ghosts: Constraining Inflation with the Parity-Odd Galaxy Four-Point Function
- Cosmology Without Window Functions: Cubic Estimators for the Galaxy Bispectrum
- Detecting Bispectral Acoustic Oscillations from Inflation Using a New Flexible Estimator
- Multiple Methods for Estimating the Bispectrum of the Cosmic Microwave Background with Application to the MAXIMA Data
- Optimal CMB Lensing Reconstruction and Parameter Estimation with SPTpol Data
- New Optimised Estimators for the Primordial Trispectrum
- Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation
- The bispectrum of polarized galactic foregrounds
- General parity-odd CMB bispectrum estimation
- The CMB Bispectrum, Trispectrum, non-Gaussianity, and the Cramer-Rao Bound
- Using inpainting to construct accurate cut-sky CMB estimators
- Power Spectrum Estimators For Large CMB Datasets
- Efficient optimal non-Gaussian CMB estimators with polarisation
- CMB B-mode non-Gaussianity: optimal bispectrum estimator and Fisher forecasts
- CMB lensing reconstruction biases from masking extragalactic sources
- Efficient Computation of -point Correlation Functions in Dimensions
- Trispectrum estimator in equilateral type non-Gaussian models
- The probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum
- Constraints on from Planck temperature and polarization
- Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum