
Hamiltonian Monte Carlo for Hierarchical Models 89
0
0.2
0.4
0.6
0.8
1
0.1 0.2 0.3 0.4 0.5
Average Acceptance Probability
Step Size
(a)
1
1.01
1.02
1.03
1.04
1.05
0.1 0.2 0.3 0.4 0.5
R
^
v
Step Size
(b)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.1 0.2 0.3 0.4 0.5
Percent Divergence
Step Size
(c)
FIGURE 4.5
Careful consideration of any adaptation procedure is crucial for valid inference
in hierarchical models. As the step size of the numerical integrator is decreased
(a) the averag e acceptance probability increases from the canonically optimal
value of 0.651 but (b) the sampler output conver ges to a consistent distribu-
tion. Indeed, (c) at the canonically optimal ...