Algorithm 2.

Hamiltonian Monte Carlo

1:
	procedure HMC(θ(0), log f(θ), M, N, ϵ, L)
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	Calculate log f(θ(0))
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	for t = 1,..., N do
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	p ← N(0, M)
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	θ(t) ← θ(t−1), θ ← θ(t−1), p ← p
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	for i = 1,..., L do
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	θ, p ← Leapfrog(θ, p, ϵ, M)
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	end for
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	$\alpha \leftarrow \min \left(1,\frac{\exp (\log f(\mathit{\theta })-\frac{1}{2}{\tilde{\mathbf{p}}}^T{\mathbf{M}}^{-1}\tilde{\mathbf{p}})}{\exp (\log f({\mathit{\theta }}^{(t-1)})-\frac{1}{2}{\mathbf{p}}^T{\mathbf{M}}^{-1}\mathbf{p})}\right)$
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	With probability α, θ(t) ← θ and p(t) ← −p
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	end for
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	return θ(1),..., θ(N)
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	function Leapfrog(θ*, p*, ϵ, M)
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	p ← p* + (ϵ / 2)∇θ log f(θ*)
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	θ ← θ* + ϵM−1p
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	p ← p + (ϵ / 2)∇θ log f(θ)
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	return θ, p
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	end function
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	end procedure