Likelihood Non-Gaussianity in Large-Scale Structure Analyses

Standard present day large-scale 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 ($P_\ell$) analysis and the Sinha et al. (2017) group multiplicity function ($\zeta$) analysis. Using non-parametric divergence estimators on mock catalogs originally constructed for covariance matrix estimation, we identify significant non-Gaussianity in both the $P_\ell$ and $\zeta$ 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 $pseudo$-likelihood. 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 non-Gaussianity shifts the $f\sigma_8$ constraint by $-0.44\sigma$, but otherwise, does not significantly impact the overall parameter constraints of Beutler et al. (2017). For the $\zeta$ analysis, using the pseudo-likelihood significantly underestimates the uncertainties and biases the constraints of Sinha et al. (2017) halo occupation parameters. For $\log M_1$ and $\alpha$, the posteriors are shifted by $+0.43\sigma$ and $-0.51\sigma$ 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 non-Gaussianity and deriving more accurate parameter constraints.Comment: 33 pages, 7 figure

The escape fraction of ionizing photons during the Epoch of Reionization:Observability with the Square Kilometre Array

One of the most important parameters in characterizing the Epoch of Reionization, the escape fraction of ionizing photons, fesc, remains unconstrained both observationally and theoretically. With recent work highlighting the impact of galaxy-scale feedback on the instantaneous value of fesc, it is important to develop a model in which reionization is self-consistently coupled to galaxy evolution. In this work, we present such a model and explore how physically motivated functional forms of fesc affect the evolution of ionized hydrogen within the intergalactic medium. Using the 21 cm power spectrum evolution, we investigate the likelihood of observationally distinguishing between a constant fesc and other models that depend upon different forms of galaxy feedback. We find that changing the underlying connection between fesc and galaxy feedback drastically alters the large-scale 21 cm power. The upcoming Square Kilometre Array Low Frequency instrument possesses the sensitivity to differentiate between our models at a fixed optical depth, requiring only 200 h of integration time focused on redshifts z = 7.5-8.5. Generalizing these results to account for a varying optical depth will require multiple 800 h observations spanning redshifts z = 7-10. This presents an exciting opportunity to observationally constrain one of the most elusive parameters during the Epoch of Reionization

Corrfunc: Blazing fast correlation functions with AVX512F SIMD Intrinsics

Correlation functions are widely used in extra-galactic astrophysics to extract insights into how galaxies occupy dark matter halos and in cosmology to place stringent constraints on cosmological parameters. A correlation function fundamentally requires computing pair-wise separations between two sets of points and then computing a histogram of the separations. Corrfunc is an existing open-source, high-performance software package for efficiently computing a multitude of correlation functions. In this paper, we will discuss the SIMD AVX512F kernels within Corrfunc, capable of processing 16 floats or 8 doubles at a time. The latest manually implemented Corrfunc AVX512F kernels show a speedup of up to $\sim 4\times$ relative to compiler-generated code for double-precision calculations. The AVX512F kernels show $\sim 1.6\times$ speedup relative to the AVX kernels and compare favorably to a theoretical maximum of $2\times$. In addition, by pruning pairs with too large of a minimum possible separation, we achieve a $\sim 5-10\%$ speedup across all the SIMD kernels. Such speedups highlight the importance of programming explicitly with SIMD vector intrinsics for complex calculations that can not be efficiently vectorized by compilers. Corrfunc is publicly available at https://github.com/manodeep/Corrfunc/.Comment: Paper II for the Corrfunc software package, paper I is on arXiv here: arXiv:1911.03545. Appeared in the refereed proceedings for the "Second Workshop on Software Challenges to Exascale Computing