Shadow Magnetic Hamiltonian Monte Carlo

Incorporating partial momentum refreshment into Magnetic Hamiltonian Monte Carlo (MHMC) to create with (PMHMC) has been shown improve the sampling performance of MHMC significantly. At same time, from an integrator-dependent shadow or modified target density utilised boost acceptance rates (HMC), which leads more efficient as integrator is better conserved by than true Hamiltonian. Sampling associated numerical used in yet be explored literature. This work aims address this gap literature combining benefits non-canonical dynamics those achieved targeting We first determine and use construct a novel method, we refer Shadow (SMHMC), that behaviour when compared while leaving distribution invariant. The new SMHMC method PMHMC across various posterior distributions, including datasets modeled using Bayesian Neural Networks Logistic Regression models.