Fast Projected Bispectra: the filter-square approach

TL;DR

This paper introduces the filtered-squared bispectrum (FSB), a fast and robust estimator for the projected bispectrum that leverages power spectrum techniques to improve efficiency and covariance estimation in large-scale structure analysis.

Contribution

The paper presents the FSB estimator, which simplifies bispectrum measurement by recycling power spectrum infrastructure and accurately estimates covariance with minimal model dependence.

Findings

FSB is computationally efficient and robust against mode-coupling effects.

Existing power spectrum covariance techniques can be adapted for bispectrum covariance estimation.

The method accurately captures Gaussian and non-Gaussian contributions in a model-independent way.

Abstract

The study of third-order statistics in large-scale structure analyses has been hampered by the increased complexity of bispectrum estimators (compared to power spectra), the large dimensionality of the data vector, and the difficulty in estimating its covariance matrix. In this paper we present the filtered-squared bispectrum (FSB), an estimator of the projected bispectrum effectively consisting of the cross-correlation between the square of a field filtered on a range of scales and the original field. Within this formalism, we are able to recycle much of the infrastructure built around power spectrum measurement to construct an estimator that is both fast and robust against mode-coupling effects caused by incomplete sky observations. Furthermore, we demonstrate that the existing techniques for the estimation of analytical power spectrum covariances can be used within this formalism to calculate the bispectrum covariance at very high accuracy, naturally accounting for the most relevant Gaussian and non-Gaussian contributions in a model-independent manner.