Table 1 Iterative Markov chain Monte Carlo Algorithm

Require: desired distribution p(·), starting value (ω⁰, λ ⁰), proposal distribution q _λ (·|λ ^(t)), number of leapfrog steps for HMC L, proposal distribution for stepsize ϵ of leapfrog steps q_ϵ(·), standard deviation σ _ρ for the sampling of the momentum variables ρ, number of Markov chain samples T

1: t ← 0

2: while t <T do

3:   Sample from q_ϵ(·)

4:   Sample from for all i ∈ {1,..., n}

5:   Perform L leapfrog steps with stepsize starting at state (ω^(t), ρ ^(t))

6:   Store resulting candidate state in

7:   Sample u₁ from (0, 1)

8:   α₁ ← min {1, exp H(ω^(t), ρ^(t)) - H)}

9:   if u₁ <α₁ then

10:      ω^(t+1)←

11:   else

12:      ω^(t+1)← ω^(t)

13:   end if

14:   Sample from q _λ (·|λ^(t))

15:   Sample u₂ from (0, 1)

16:   

17:   if u₂ <α₂ then

18:      λ^(t+1)←

19:   else

20:      λ^(t+1)← λ^(t)

21:   end if

22:   Append (ω^(t+1), λ^(t+1)) to Markov chain

23:   t ← t + 1

24: end while

25: return Markov chain