1887

Abstract

The Hamiltonian Monte Carlo (HMC) algorithm is a Markov Chain Monte Carlo (MCMC) technique, which combines the advantages of Hamiltonian dynamics methods and Metropolis Monte Carlo approach, to sample from complex distributions. The HMC algorithm incorporates gradient information in the dynamic trajectories and thus suppresses the random walk nature in traditional Markov chain simulation methods. This ensures rapid mixing, faster convergence, and improved efficiency of the Markov chain. The leapfrog method is generally used in discrete simulation of the dynamic transitions. In this paper, we refer to this as the leapfrog–HMC. The primary goal of this paper is to present the HMC algorithm as a tool for rapid sampling of high dimensional and complex distributions, and demonstrate its advantages over the classical Metropolis Monte Carlo technique. We demonstrate that the use of an adaptive–step discretization scheme in simulating the dynamic transitions results in an algorithm which significantly outperforms the leapfrog–HMC algorithm. Relevance to reservoir parameter estimation and uncertainty quantification will be discussed.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20146437
2008-09-08
2021-09-20
Loading full text...

Full text loading...

http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20146437
Loading
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error