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 />
Improving Phase–Space Sampling<br />
Improvement Strategies<br />
Variable <strong>Step</strong>–Size <strong>HMC</strong> <strong>Algorithm</strong> (SV<strong>HMC</strong>)<br />
Explicit variable step–size using a Runge–Kutta scheme<br />
<strong>Adaptive</strong> Störmer–Verlet<br />
For l = 1 : L − steps<br />
End For<br />
C l+<br />
1 = C l + ɛ P<br />
2 2ρ l+<br />
1 ,<br />
l 2<br />
P l+<br />
1 = P l − ɛ ∇V(C<br />
2 2ρ l ),<br />
l<br />
ρ l+1 + ρ l = 2U(C l+<br />
1<br />
2<br />
P l+1 = P l+<br />
1 −<br />
2<br />
, P l+<br />
1 ),<br />
2<br />
ɛ<br />
2ρ l+1<br />
∇V(C l+1 ),<br />
C l+1 = C l+<br />
1 + ɛ P<br />
2 2ρ l+<br />
1 .<br />
n+1 2<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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