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Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Scalar Edition

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arxiv 2303.08828 v2 pith:JW7LC2RA submitted 2023-03-15 astro-ph.CO gr-qchep-phhep-th

classification astro-ph.COgr-qchep-phhep-th
keywords estimatorsoptimalarbitraryincludescalartrispectrumweightingaccompanying
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dissecting the Scalar Cosmological Collider with the Cosmic Microwave Background

    astro-ph.CO 2026-07 accept novelty 7.0 of 10

    A joint Bayesian fit of the multi-field inflationary Lagrangian to Planck bispectrum data finds no cosmological collider signal (max Δχ²=5.3) and shows weak-mixing template searches are invalid except at the smallest masses.

  2. Searching for Inflationary Physics with the CMB Trispectrum: 2. Code & Validation

    astro-ph.CO 2025-02 conditional novelty 7.0 of 10

    PolySpec is a public, validated suite of near-optimal quartic estimators that lets the CMB four-point function probe many inflationary models beyond local non-Gaussianity.

  3. Searching for Inflationary Physics with the CMB Trispectrum: 1. Primordial Theory & Optimal Estimators

    astro-ph.CO 2025-02 conditional novelty 7.0 of 10

    A set of quasi-optimal CMB trispectrum estimators is derived for local, EFT, direction-dependent, spinning-particle, point-source, and lensing templates, enabling first collider searches.

  4. Searching for Inflationary Physics with the CMB Trispectrum: 3. Constraints from Planck

    astro-ph.CO 2025-02 accept novelty 6.0 of 10

    A comprehensive Planck PR4 trispectrum analysis finds no primordial non-Gaussianity across 33 templates and sets leading constraints, including tau_NL loc < 1500 at 95% CL.

  5. An optimal quadratic estimator for window-free cosmic shear power spectra

    astro-ph.CO 2026-07 conditional novelty 5.0 of 10

    A window-free quadratic estimator that is statistically optimal when the true covariance is known improves cosmic shear E-mode precision by 5–15% at ℓ≲500 and suppresses E→B leakage.

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