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Input: y, I, Ib, θ^(0) = {c^(0), t^(0), σ_e^(0)}

for i = 1 to I + Ib do
    for k = 1 to K do
        c_k^(i) ~ p(c_k | c_1^(i), c_2^(i), ..., c_(k-1)^(i), c_(k+1)^(i-1), ..., c_K^(i-1), t^(i-1), σ_e^(i-1), y)
    end for
    for k = 1 to K do
        t_k^(i) ~ p(t_k | c^(i), t_1^(i), ..., t_(k-1)^(i), t_(k+1)^(i-1), ..., t_K^(i-1), σ_e^(i-1), y)
    end for
    σ_e^(i) ~ p(σ_e | c^(i), t^(i), y)
end for
θ̂_MMSE = Compute_MMSE_estimate(θ)

plaintext Copy code Input: y, I, Ib, θ^(0) = {c^(0), t^(0), σ_e^(0)} for i = 1 to I + Ib do for k = 1 to K do // Sample c_k^(i) from its conditional posterior c_k^(i) ~ p(c_k | c_1^(i), c_2^(i), ..., c_(k-1)^(i), c_(k+1)^(i-1), ..., c_K^(i-1), t^(i-1), σ_e^(i-1), y) end for for k = 1 to K do // Sample t_k^(i) from its conditional posterior t_k^(i) ~ p(t_k | c^(i), t_1^(i), ..., t_(k-1)^(i), t_(k+1)^(i-1), ..., t_K^(i-1), σ_e^(i-1), y) end for // Sample σ_e^(i) from its conditional posterior σ_e^(i) ~ p(σ_e | c^(i), t^(i), y) end for // Compute the MMSE estimate using (10) θ̂_MMSE = Compute_MMSE_estimate(θ)

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