Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretisation of Hamiltonian equations motion (EoM). This is achieved by recursively applying basic second-order leap-frog scheme (considering single evaluation EoM) in a combination even numbers forward time steps with intermediate backward step. largely reduces number evaluations and random gradient computations, as required usual case for high-dimensional cases. restrict this to lognormal-Poisson model, applied full volume halo catalogue real space on cubical mesh 1250 $h^{-1}$ Mpc side 256$^3$ cells. Hence, neglect selection effects, redshift distortions, displacements. note that those observational evolution effects can be accounted subsequent Gibbs-sampling COSMIC BIRTH algorithm. find going from second shortens burn-in phase factor at least $\sim30$. implies 75-90 independent samples are obtained while fastest method converges. After convergence, correlation lengths indicate an improvement about 3.0 fewer computations meshes considered cosmological scenario, traditional turns out outperform schemes only lower dimensional problems, e.g. 64$^3$ gain computational efficiency help go towards analysis large-scale structure upcoming galaxy surveys.