MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD

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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 ... continued below

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245 Kilobytes pages

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HANSON, K. February 1, 2001.

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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.

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245 Kilobytes pages

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  • Report No.: LA-UR-01-1016
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 775292
  • Archival Resource Key: ark:/67531/metadc715942

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  • February 1, 2001

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  • Sept. 29, 2015, 5:31 a.m.

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  • March 22, 2016, 3:38 p.m.

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HANSON, K. MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD, article, February 1, 2001; New Mexico. (digital.library.unt.edu/ark:/67531/metadc715942/: accessed January 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.