Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis. Issue 3 (21st January 2021)

• Record Type: Journal Article
• Authors: Hernández-Sánchez, Mónica; Kitaura, Francisco-Shu; Ata, Metin; Dalla Vecchia, Claudio
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 502:Issue 3(2021)
• Page Start: 3976
• Page End: 3992
• Publication Date: 2021-01-21
• Subjects: methods: data analysis -- methods: numerical -- methods: statistical -- large-scale structure of Universe -- cosmology: observations; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stab123
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h −1 Mpc side and 256 3 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 256 3 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 64 3 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.