MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD
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 {var_phi}, where {var_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 {var_phi} and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. The efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs is shown to remain 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 {var_phi}, is proposed to measure the convergence of the MCMC sequence.
- Research Organization:
- Los Alamos National Lab., NM (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 775292
- Report Number(s):
- LA-UR-01-1016
- Country of Publication:
- United States
- Language:
- English
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