The HMC Algorithm with Overrelaxation and Adaptive--Step ...
The HMC Algorithm with Overrelaxation and Adaptive--Step ...
The HMC Algorithm with Overrelaxation and Adaptive--Step ...
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Background<br />
Aim of Talk<br />
<strong>The</strong> Hamiltonian Monte Carlo (<strong>HMC</strong>) <strong>Algorithm</strong><br />
Improving Performance of <strong>HMC</strong> <strong>Algorithm</strong><br />
Numerical Experiments & Results<br />
Numerical Experiments<br />
Example results from the improved <strong>HMC</strong> algorithm<br />
Gaussian targets <strong>with</strong> uncorrelated covariates in 64 &<br />
128D<br />
(<br />
1<br />
π(C) =<br />
exp − 1 )<br />
(2π) D 2 det(Σ) 1 2 2 CT Σ −1 C . (13)<br />
Compare <strong>HMC</strong>, SV<strong>HMC</strong> & OSV<strong>HMC</strong> algorithms based on<br />
Degree of chain autocorrelation<br />
Effective number of samples in a given chain<br />
Variance of sample means, C, of a finite chain<br />
Convergence rates/ratio<br />
Dimensionless efficiency,<br />
M. Alfaki, S. Subbey, <strong>and</strong> D. Haugl<strong>and</strong> <strong>The</strong> Hamiltonian Monte Carlo (<strong>HMC</strong>) <strong>Algorithm</strong>
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