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Hamiltonian Monte Carlo  

2014-02-10 15:07:32|  分类: Data Analysis |  标签: |举报 |字号 订阅

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MCMC algorithm such as Metropolis-Hastings are simple, but have disadvantages such as low acceptance-ratio, poor mixing, so lots of time and computer resources are usually wasted...

Hamiltonian Monte Carlo (S.Duan, et al, 1987) is a slightly more advantaged algorithm, using the concept of Hamiltonian mechanics, with momentum variables augmented.  By evolving this dynamical system, it is always possible to sample points in the parameter space with a high acceptance probability.

The following is an example of a two-dimensional harmonic system..., the trajectories are positions and velocities in two dimensions

Hamiltonian Monte Carlo - Dreamer - Do Things Right

 here this a sampled result of x1 and x2

Hamiltonian Monte Carlo - Dreamer - Do Things Right
 
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