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

−3
10 10−2 10−1 100 101
Background
Aim of Talk
The Hamiltonian Monte Carlo (HMC) Algorithm
Improving Performance of HMC Algorithm
Numerical Experiments & Results
Example results from the improved HMC algorithm
Evaluation criteria – Geometric Illustration
Degree of correlation
Spectral analysis
Autocorrelation function
0.9
0.7
0.5
10 0
ρ(τ)
0.3
P(κ)
0.1
10 −1
−0.1
−0.3
−0.5
0 1 2 3 4 5 6 7 8
τ
10 1 κ
10−2
−3
10 10−2 10−1 100 101
1.3
Integrated autocorrelation function
The curve turn over
1.1
ρ int
(τ)
0.9
10 0
10 1 κ
P(0)
P(κ)
P(κ)≈ (κ) −α
0.7
0.5
0.3
0 1 2 3 4 5 6 7 8
τ
κ*
M. Alfaki, S. Subbey, and D. Haugland The Hamiltonian Monte Carlo (HMC) Algorithm