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

1.9
1.7
1.5
1.3
1.1
0.9
0.7
0.5
Background
Aim of Talk
The Hamiltonian Monte Carlo (HMC) Algorithm
Improving Performance of HMC Algorithm
Numerical Experiments & Results
Comparing OHMC vs HMC
Example results from the improved HMC algorithm
Gaussian Target
1
π(x) = exp ( − 1 (2π) n/2 |Σ| 1/2 2 xT Σ −1 x )
Σ = I
Results (n=64, N=2000)
OHMC HMC Ideal
Accept. rate 0.99 0.99 1
P(0) 1.35 1.51 1
κ ∗ 1.65 1.45
CPU time[sec] 561.22 557.38
E 0.74 0.66 1
r 6.7e − 4 7.6e − 4 < 0.01
τ int 1.63 1.85 0.5
N eff 614 542 2000
Graphical Illustration
P(κ)
ρ int
(τ)
3.1623
2.5119
1.9953
1.5849
1.2589
1
0.7943
0.631
0.5012
0.3981
0.3162
10 −3 10 −2 10 −1 10 0 10 1
κ
OHMC
HMC
0.3
0 2 4 6 8 10 12 14 16
τ
iacf OHMC
(τ*,τ* int
) OHMC
iacf HMC
(τ*,τ* int
) HMC
M. Alfaki, S. Subbey, and D. Haugland The Hamiltonian Monte Carlo (HMC) Algorithm