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Table 1 Iterative Markov chain Monte Carlo Algorithm

From: Reconstructing nonlinear dynamic models of gene regulation using stochastic sampling

Algorithm 1 Iterative Hybrid Monte Carlo and Metropolis Hastings 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 qϵ(·), 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 qϵ(·)
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:   tt + 1
24: end while
25: return Markov chain