Towards cosmological constraints from the compressed modal bispectrum: a
  robust comparison of real-space bispectrum estimators
  Higher-order clustering statistics, like the galaxy bispectrum, can add
complementary cosmological information to what is accessible with two-point
statistics, like the power spectrum. While the standard way of measuring the
bispectrum involves estimating a bispectrum value in a large number of Fourier
triangle bins, the compressed modal bispectrum approximates the bispectrum as a
linear combination of basis functions and estimates the expansion coefficients
on the chosen basis. In this work, we compare the two estimators by using
parallel pipelines to analyze the real-space halo bispectrum measured in a
suite of $N$-body simulations corresponding to a total volume of $\sim 1{,}000
\,h^{-3}\,{\rm Gpc}^3$, with covariance matrices estimated from 10,000 mock
halo catalogs. We find that the modal bispectrum yields constraints that are
consistent and competitive with the standard bispectrum analysis: for the halo
bias and shot noise parameters within the tree-level halo bispectrum model up
to $k_{\rm max} \approx 0.06 \, (0.10) \,h\,{\rm Mpc}^{-1}$, only 6 (10) modal
expansion coefficients are necessary to obtain constraints equivalent to the
standard bispectrum estimator using $\sim$ 20 to 1,600 triangle bins, depending
on the bin width. For this work, we have implemented a modal estimator pipeline
using Markov Chain Monte Carlo simulations for the first time, and we discuss
in detail how the parameter posteriors and modal expansion are robust to, or
sensitive to, several user settings within the modal bispectrum pipeline. The
combination of the highly efficient compression that is achieved and the large
number of mock catalogs available allows us to quantify how our modal
bispectrum constraints depend on the number of mocks that are used to estimate
covariance matrices and the functional form of the likelihood.
