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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1.7<br />
1.5<br />
1.3<br />
1.1<br />
0.9<br />
0.7<br />
0.5<br />
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 />
Comparing OSV<strong>HMC</strong> vs SV<strong>HMC</strong><br />
Example results from the improved <strong>HMC</strong> algorithm<br />
Graphical Illustration<br />
Numerical Results (n=64, N=2000)<br />
OSV<strong>HMC</strong> SV<strong>HMC</strong> Ideal<br />
Accept. rate 0.92 0.94 1<br />
P(0) 1.02 1.11 1<br />
κ ∗ 4.15 3.19<br />
CPU time[sec] 639.58 669.40<br />
E 0.98 0.90 1<br />
r 5.1e − 4 5.6e − 4 < 0.01<br />
τ int 0.71 0.94 0.5<br />
N eff 1400 1059 2000<br />
P(κ)<br />
ρ int<br />
(τ)<br />
3.1623<br />
2.5119<br />
1.9953<br />
1.5849<br />
1.2589<br />
1<br />
0.7943<br />
0.631<br />
0.5012<br />
0.3981<br />
0.3162<br />
10 −3 10 −2 10 −1 10 0 10 1<br />
κ<br />
OSV<strong>HMC</strong><br />
SV<strong>HMC</strong><br />
iacf OSV<strong>HMC</strong><br />
(τ,τ int<br />
) OSV<strong>HMC</strong><br />
iacf SV<strong>HMC</strong><br />
(τ*,τ* int<br />
) SV<strong>HMC</strong><br />
0.3<br />
0 1 2 3 4 5 6 7 8<br />
τ<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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