A Multi-Trajectory Monte Carlo Sampler

Xiaopeng Xu,
Chuancai Liu,
Hongji Yang,
Xiaochun Zhang,

Abstract


Markov Chain Monte Carlo techniques based on Hamiltonian dynamics can sample the first or last principal components of multivariate probability models using simulated trajectories. However, when components’ scales span orders of magnitude, these approaches may be unable of accessing all components adequately. While it is possible to reconcile the first and last components by alternating between two different types of trajectories, the sampling of intermediate components may be imprecise. In this paper, a function generalizing the kinetic energies of Hamiltonian Monte Carlo and Riemannian Manifold Hamiltonian Monte Carlo is proposed, and it is found that the methods based on a specific form of the function can more accurately sample normal distributions. Additionally, the multi-particle algorithm’s reasoning is given after a review of some statistical ideas.

Keywords


Hamiltonian dynamics, Kinetic energy, multi-particle system, Positive definite, Hessian

Citation Format:
Xiaopeng Xu, Chuancai Liu, Hongji Yang, Xiaochun Zhang, "A Multi-Trajectory Monte Carlo Sampler," Journal of Internet Technology, vol. 23, no. 5 , pp. 1117-1128, Sep. 2022.

Refbacks

  • There are currently no refbacks.





Published by Executive Committee, Taiwan Academic Network, Ministry of Education, Taipei, Taiwan, R.O.C
JIT Editorial Office, Office of Library and Information Services, National Dong Hwa University
No. 1, Sec. 2, Da Hsueh Rd., Shoufeng, Hualien 974301, Taiwan, R.O.C.
Tel: +886-3-931-7314  E-mail: jit.editorial@gmail.com