Abstract
The diffusive behaviour of simple random-walk proposals of many Markov Chain
Monte Carlo (MCMC) algorithms results in slow exploration of the state space making inefficient
the convergence to a target distribution. Hamiltonian/Hybrid Monte Carlo (HMC), by introducing fictious momentum variables, adopts Hamiltonian dynamics, rather than a probability distribution, to propose future states in the Markov chain. Splitting schemes are numerical integrators for
Hamiltonian problems that may advantageously replace the St¨ormer-Verlet method within HMC
methodology. In this paper a family of stable methods for univariate and multivariate Gaussian distributions, taken as guide-problems for more realistic situations, is proposed. Differently from similar
methods proposed in the recent literature, the considered schemes are featured by null expectation
of the random variable representing the energy error. The effectiveness of the novel procedures is
shown for bivariate and multivariate test cases taken from the literature.
Anno
2021
Autori IAC
Tipo pubblicazione
Altri Autori
Fasma Diele