The HMC Algorithm with Overrelaxation and Adaptive--Step ...

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Background Aim of Talk The Hamiltonian Monte Carlo (HMC) Algorithm Improving Performance of HMC Algorithm Numerical Experiments & Results Investigate Two Approaches Improving Phase–Space Sampling Improvement Strategies Proposal 1: Suppressing random Walk in Gibbs sampling Ordered over-relaxation (R. Neal) Proposal 2: Using a variable step–size for dynamics Investigate a Runge–Kutta type integrator (simplectic) M. Alfaki, S. Subbey, and D. Haugland The Hamiltonian Monte Carlo (HMC) Algorithm
Background Aim of Talk The Hamiltonian Monte Carlo (HMC) Algorithm Improving Performance of HMC Algorithm Numerical Experiments & Results Improving Phase–Space Sampling Improvement Strategies Applying over–relaxation to P– Over-rel. HMC (OHMC) Ordered over-relaxation To over–relax R n ∋ P ∼ N (P; 0, I) For i = 1 : n Generated K values from N (q i |{q j } i̸=j ). Order K values and the odd value P i . q (0) i ≤ · · · ≤ q (r) i = P i ≤ · · · ≤ q (K) i Set P ′ i = q(K−r) i . End for Example C 2 C 2 3 2 1 0 −1 −2 δπ(x 1 ,x 2 ) OHMC points OHMC −3 −3 −2 −1 0 1 2 3 C 1 3 2 1 0 −1 −2 δπ(x 1 ,x 2 ) HMC points HMC −3 −3 −2 −1 0 1 2 3 C 1 M. Alfaki, S. Subbey, and D. Haugland The Hamiltonian Monte Carlo (HMC) Algorithm
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