Full Content is available to subscribers

Subscribe/Learn More  >
Proceedings Article

Markov chain Monte Carlo posterior sampling with the Hamiltonian method

[+] Author Affiliations
Kenneth M. Hanson

Los Alamos National Lab. (USA)

Proc. SPIE 4322, Medical Imaging 2001: Image Processing, 456 (July 3, 2001); doi:10.1117/12.431119
Text Size: A A A
From Conference Volume 4322

  • Medical Imaging 2001: Image Processing
  • Milan Sonka; Kenneth M. Hanson
  • San Diego, CA | February 17, 2001

abstract

The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy (phi) , where (phi) is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of (phi) and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. I show that the efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs remains constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of (phi) , is proposed to measure the convergence of the MCMC sequence.

© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Citation

Kenneth M. Hanson
"Markov chain Monte Carlo posterior sampling with the Hamiltonian method", Proc. SPIE 4322, Medical Imaging 2001: Image Processing, 456 (July 3, 2001); doi:10.1117/12.431119; http://dx.doi.org/10.1117/12.431119


Access This Proceeding
Sign in or Create a personal account to Buy this proceeding ($15 for members, $18 for non-members).

Figures

Tables

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Proceeding
Sign in or Create a personal account to Buy this proceeding ($15 for members, $18 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.