Higher order Hamiltonian Monte Carlo sampling for cosmological largescale structure analysis
Abstract
We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourthorder discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic secondorder leapfrog 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 secondorder case for highdimensional cases. We restrict this study to the lognormalPoisson 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 Gibbssampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leapfrog scheme shortens the burnin phase by a factor of at least ∼30. This implies that 7590 independent samples are obtained while the fastest secondorder 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 leapfrog 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 largescale structure for upcoming galaxy surveys.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 April 2021
 DOI:
 10.1093/mnras/stab123
 arXiv:
 arXiv:1911.02667
 Bibcode:
 2021MNRAS.502.3976H
 Keywords:

 methods: data analysis;
 methods: numerical;
 methods: statistical;
 largescale structure of Universe;
 cosmology: observations;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Lattice
 EPrint:
 19 pages, 12 figures, 4 tables, accepted at MNRAS, additional robust mathematical argument supported by numerical tests with longer HMC chains and a solid statistical analysis