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 />
<strong>Algorithm</strong> Description–II<br />
Practical Implementation<br />
If V(C) induces a Boltzmann distribution over C<br />
p(C) =<br />
e −V(C)<br />
∫<br />
R<br />
e −V(C) dC<br />
n<br />
(6)<br />
H(C, P) induces a similar distribution on (C, P),<br />
p(C, P) =<br />
e −H(C,P)<br />
∫R<br />
∫R<br />
e −H(C,P) = p(C)p(P), (7)<br />
dCdP n n<br />
p(P) = (2π) −n/2 e (− 1 2 |P|2) . (8)<br />
Simulate ergodic Markov chain <strong>with</strong> stationary distrib. ∼ (7)<br />
Estimate 〈J〉– use values of C from successive Markov<br />
chain states <strong>with</strong> marginal distribution given by (6)<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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