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The Geometry of Hamiltonian Monte Carlo

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arxiv 1112.4118 v1 pith:ZXLYZQU3 submitted 2011-12-18 stat.ME physics.data-an

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keywords carlohamiltonianmontechainchoicegeometrymarkovadmissible
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With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately contingent on the choice of a suitable Hamiltonian function. By examining both the symplectic geometry underlying Hamiltonian dynamics and the requirements of Markov Chain Monte Carlo, we construct the general form of admissible Hamiltonians and propose a particular choice with potential application in Bayesian inference.

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    SSMProblems.jl and GeneralisedFilters.jl provide a unified Julia interface for defining state space models and running Kalman, particle, and Rao-Blackwellised filter inference with GPU support.

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