Toward a robust inference method for the galaxy bispectrum: likelihood function and model selection
Andrea Oddo, Emiliano Sefusatti, Cristiano Porciani, Pierluigi Monaco, Ariel G. Sánchez
备注：
38 pages, 17 figures; major revisions: inclusion of open triangle bins in all results, new priors for the shot-noise parameters, and additional comparison with Gaussian variance
发表信息：
Journal of Cosmology and Astroparticle Physics, Issue 03, article id. 056 (2020)
The forthcoming generation of galaxy redshift surveys will sample the large-scale structure of the Universe over unprecedented volumes with high-density tracers. This advancement will make robust measurements of three-point clustering statistics possible. In preparation for this improvement, we investigate how several methodological choices can influence inferences based on the bispectrum about galaxy bias and shot noise. We first measure the real-space bispectrum of dark-matter haloes extracted from 298 N-body simulations covering a volume of approximately $1000 h^{-3} \mathrm{Gpc}^3$. We then fit a series of theoretical models based on tree-level perturbation theory to the numerical data. To achieve this, we estimate the covariance matrix of the measurement errors by using 10,000 mock catalogues generated with the Pinocchio code. We study how the model constraints are influenced by the binning strategy for the bispectrum configurations and by the form of the likelihood function. We also use Bayesian model-selection techniques to single out the optimal theoretical description of our data. We find that a three-parameter bias model combined with Poissonian shot noise is necessary to model the halo bispectrum up to scales of $k_\mathrm{max}\lesssim 0.08 h \mathrm{Mpc}^{-1}$, although fitting formulae that relate the bias parameters can be helpful to reduce the freedom of the model without compromising accuracy. Our data clearly disfavour local Eulerian and local Lagrangian bias models and do not require corrections to Poissonian shot noise. We anticipate that model-selection diagnostics will be particularly useful to extend the analysis to smaller scales as, in this case, the number of model parameters will grow significantly large.
We present a joint likelihood analysis of the halo power spectrum and bispectrum in real space. We take advantage of a large set of numerical simulations and of an even larger set of halo mock catalogs to provide a robust estimate of the covariance properties. We derive constraints on bias and cosmological parameters assuming a theoretical model from perturbation theory at one-loop for the power spectrum and tree-level for the bispectrum. By means of the Deviance Information Criterion, we select a reference bias model dependent on seven parameters that can describe the data up to $k_{\rm max,P…
We present the complete expression for the next-to-leading (1-loop) order galaxy power spectrum and the leading-order galaxy bispectrum in redshift space in the general bias expansion, or equivalently the effective field theory of biased tracers. We consistently include all line-of-sight dependent selection effects. These are degenerate with many, but not all, of the redshift-space distortion contributions, and have not been consistently derived before. Moreover, we show that, in the framework of effective field theory, a consistent bias expansion in redshift space must include these selection…
Upcoming galaxy redshift surveys promise to significantly improve current limits on primordial non-Gaussianity (PNG) through measurements of 2- and 3-point correlation functions in Fourier space. However, realizing the full potential of this dataset is contingent upon having both accurate theoretical models and optimized analysis methods. Focusing on the local model of PNG, parameterized by $f_{\rm NL}$, we perform a Monte-Carlo Markov Chain analysis to confront perturbation theory predictions of the halo power spectrum and bispectrum in real space against a suite of N-body simulations. We mod…
We present a Fisher information study of the statistical impact of galaxy bias and selection effects on the estimation of key cosmological parameters from galaxy redshift surveys; in particular, the angular diameter distance, Hubble parameter, and linear growth rate at a given redshift, the cold dark matter density, and the tilt and running of the primordial power spectrum. The line-of-sight-dependent selection contributions we include here are known to exist in real galaxy samples. We determine the maximum wavenumber included in the analysis by requiring that the next-order corrections to the…
Halving and Doubling: Boosting the Detection of Relativistic Effects in the Galaxy Bispectrum with Optimal Subsample Selection
Università degli Studi di Torino（都灵大学）；INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino（意大利国家核物理研究所都灵分部）；INAF – Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino（意大利国家天体物理学研究所都灵天文台）；University of the Western Cape（西开普敦大学）；Queen Mary University of London（伦敦玛丽女王大学）；Università degli Studi di Ferrara（费拉拉大学）
We present the first application of the isosceles bispectrum to MCMC parameter inference from the cosmic 21-cm signal. We extend the MCMC sampler 21cmMC to use the fast bispectrum code, BiFFT, when computing the likelihood. We create mock 1000h observations with SKA1-low, using PyObs21 to account for uv-sampling and thermal noise. Assuming the spin temperature is much higher than that of the CMB, we consider two different reionization histories for our mock observations: fiducial and late-reionization. For both models we find that bias on the inferred parameter means and 1-$σ$ credible interva…
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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 me…
We present a joint likelihood analysis of the real-space power spectrum and bispectrum measured from a variety of halo and galaxy mock catalogs. A novel aspect of this work is the inclusion of nonlinear triangle configurations for the bispectrum, made possible by a complete next-to-leading order ("one-loop") description of galaxy bias, as is already common practice for the power spectrum. Based on the goodness-of-fit and the unbiasedness of the parameter posteriors, we accomplish a stringent validation of this model compared to the leading order ("tree-level") bispectrum. Using measurement unc…
When analyzing the galaxy bispectrum measured from spectroscopic surveys, it is imperative to account for the effects of non-uniform survey geometry. Conventionally, this is done by convolving the theory model with the the window function; however, the computational expense of this prohibits full exploration of the bispectrum likelihood. In this work, we provide a new class of estimators for the unwindowed bispectrum; a quantity that can be straightforwardly compared to theory. This builds upon the work of Philcox (2021) for the power spectrum, and comprises two parts (both obtained from an Ed…
We apply two compression methods to the galaxy power spectrum monopole/quadrupole and bispectrum monopole measurements from the BOSS DR12 CMASS sample. Both methods reduce the dimension of the original data-vector to the number of cosmological parameters considered, using the Karhunen-Loève algorithm with an analytic covariance model. In the first case, we infer the posterior through MCMC sampling from the likelihood of the compressed data-vector (MC-KL). The second, faster option, works by first Gaussianising and then orthogonalising the parameter space before the compression; in this option …
We perform a joint analysis of the power spectrum and the bispectrum of the CMB temperature and polarization anisotropies to improve the constraints on isocurvature modes. We construct joint likelihoods, both for the existing Planck data, and to make forecasts for the future LiteBIRD and CMB-S4 experiments. We assume a general two-field inflation model with five free parameters, leading to one isocurvature mode (which can be CDM density, neutrino density or neutrino velocity) arbitrarily correlated with the adiabatic mode. We theoretically assess in which cases (of detecting and/or fixing para…
Upcoming cosmic microwave background (CMB) lensing measurements and tomographic galaxy surveys are expected to provide us with high-precision data sets in the coming years, thus paving the way for fruitful cross-correlation analyses. In this paper we study the information content of the weighted skew-spectrum, a nearly-optimal estimator of the angular bispectrum amplitude, as a means to extract non-Gaussian information on both bias and cosmological parameters from the bispectra of galaxies cross-correlated with CMB lensing, while gaining significantly on speed. Our results show that for the co…
We study the cosmological information content of the redshift-space galaxy bispectrum monopole at one-loop order in perturbation theory. We incorporate all effects necessary for comparison to data: fourth-order galaxy bias, infrared resummation (accounting for the non-linear evolution of baryon acoustic oscillations), ultraviolet counterterms, non-linear redshift-space distortions, stochastic contributions, projection, and binning effects. The model is implemented using FFTLog, and validated with the PT Challenge suite of $N$-body simulations, whose large volume allows for high-precision tests…
Conventional approaches to cosmology inference from galaxy redshift surveys are based on n-point functions, which are under rigorous perturbative control on sufficiently large scales. Here, we present an alternative approach, which employs a likelihood at the level of the galaxy density field. By integrating out small-scale modes based on effective-field theory arguments, we prove that this likelihood is under perturbative control if certain specific conditions are met. We further show that the information captured by this likelihood is equivalent to the combination of the next-to-leading orde…
We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all stochastic terms apart from the ones appearing in the auto two-point function of tracers, we recover the result of Schmidt et al., 2018. We then rigorously derive the corrections to this result, such as those coming from a non-Gaussian stochasticity (which include the stochastic corrections to the tracer bispectrum) and higher-derivative terms. We discuss how …
We present a Markov-Chain Monte-Carlo (MCMC) forecast for the precision of neutrino mass and cosmological parameter measurements with a Euclid-like galaxy clustering survey. We use a complete perturbation theory model for the galaxy one-loop power spectrum and tree-level bispectrum, which includes bias, redshift space distortions, IR resummation for baryon acoustic oscillations and UV counterterms. The latter encapsulate various effects of short-scale dynamics which cannot be modeled within perturbation theory. Our MCMC procedure consistently computes the non-linear power spectra and bispectra…
Multi-messenger observations of binary neutron star mergers offer a promising path towards resolution of the Hubble constant ($H_0$) tension, provided their constraints are shown to be free from systematics such as the Malmquist bias. In the traditional Bayesian framework, accounting for selection effects in the likelihood requires calculation of the expected number (or fraction) of detections as a function of the parameters describing the population and cosmology; a potentially costly and/or inaccurate process. This calculation can, however, be bypassed completely by performing the inference …
Reanalyzing DESI DR1: 1. $Λ$CDM Constraints from the Power Spectrum and Bispectrum
Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève（日内瓦大学理论物理系与天体粒子物理中心）；Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯研究所理论物理中心）；Simons Society of Fellows, Simons Foundation（西蒙斯基金会西蒙斯学者协会）；Center for Theoretical Physics, Columbia University（哥伦比亚大学理论物理中心）；Leinweber Institute for Theoretical Physics at Stanford（斯坦福大学莱因韦伯理论物理研究所）
We have developed a new Bayesian method to correct the flux densities of astronomical sources. The hybrid method combines a simulated likelihood to model survey selection together with an analytic source-count-based prior. The simulated likelihood captures the effect of complicated selection methods, such as multi-frequency filtering or imposed restrictions on recovered sample properties (e.g., color cuts). Simulations are also able to capture unanticipated sources of uncertainty. In this way, the method enables a broader application of Bayesian techniques. Use of an analytic prior allows vari…
