Abstract
Standard presentday largescale structure (LSS) analyses make a major assumption in their Bayesian parameter inference  that the likelihood has a Gaussian form. For summary statistics currently used in LSS, this assumption, even if the underlying density field is Gaussian, cannot be correct in detail. We investigate the impact of this assumption on two recent LSS analyses: the Beutler et al. (2017) power spectrum multipole (Pℓ) analysis and the Sinha et al. (2017) group multiplicity function (ζ) analysis. Using nonparametric divergence estimators on mock catalogs originally constructed for covariance matrix estimation, we identify significant nonGaussianity in both the Pℓ and ζ likelihoods. We then use Gaussian mixture density estimation and Independent Component Analysis on the same mocks to construct likelihood estimates that approximate the true likelihood better than the Gaussian pseudolikelihood. Using these likelihood estimates, we accurately estimate the true posterior probability distribution of the Beutler et al. (2017) and Sinha et al. (2017) parameters. Likelihood nonGaussianity shifts the fσ8 constraint by −0.44σ, but otherwise, does not significantly impact the overall parameter constraints of Beutler et al. (2017). For the ζ analysis, using the pseudolikelihood significantly underestimates the uncertainties and biases the constraints of Sinha et al. (2017) halo occupation parameters. For logM1 and α, the posteriors are shifted by +0.43σ and −0.51σ and broadened by 42% and 66%, respectively. The divergence and likelihood estimation methods we present provide a straightforward framework for quantifying the impact of likelihood nonGaussianity and deriving more accurate parameter constraints.
Original language  English 

Pages (fromto)  29562969 
Number of pages  14 
Journal  Monthly Notices of the Royal Astronomical Society 
Volume  485 
Issue number  2 
Early online date  26 Feb 2019 
DOIs  
Publication status  Published  1 May 2019 
Keywords
 Cosmological parameters
 Cosmology: Observations
 Galaxies: Statistics
 Largescale structure of Universe
 Methods: Data analysis
 Methods: Statistical
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Data availability statement for 'Likelihood nonGaussianity in largescale structure analyses'.
Hahn, C. H. (Creator), Beutler, F. (Creator), Sinha, M. (Creator), Berlind, A. A. (Creator), Ho, S. (Creator) & Hogg, D. W. (Creator), Oxford University Press, 1 May 2019
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