Soft x-ray diffraction of striated muscle
S.F. Fan, W.B. Yun, et al.
Proceedings of SPIE 1989
We establish L « {L^{\mathfrak{q}}} convergence for Hamiltonian Monte Carlo (HMC) algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ « < ∞ {2\leq\mathfrak{q}<\infty} and weakly for 1 < « < 2 {1<\mathfrak{q}<2}) to the desired target distribution. In addition, we establish a general convergence rate for an L « {L^{\mathfrak{q}}} convergence given a convergence rate at a specific q ∗ {q^{∗}}, and apply this result to conclude geometric convergence in the Euclidean space for HMC with uniformly strongly logarithmic concave target and auxiliary distributions. We also present the results of experiments to illustrate convergence in L « {L^{\mathfrak{q}}}.
S.F. Fan, W.B. Yun, et al.
Proceedings of SPIE 1989
Zhihua Xiong, Yixin Xu, et al.
International Journal of Modelling, Identification and Control
David Cash, Dennis Hofheinz, et al.
Journal of Cryptology
J. LaRue, C. Ting
Proceedings of SPIE 1989