Algorithm 1.

Estimation of the general and individual cortical thickness decrease with the MCMC-SAEM algorithm.

Input: Longitudinal dataset y = (yi,j)i, j of measurement maps, with the corresponding ages (ti,j)i, j.

Initial parameters θ0 and latent variables z0.

Geometrically decreasing sequence of step-sizes ${\rho }^k$.

Sufficient statistics $S^k$

Initialization: set k = 0 and S0 = S(z0).

repeat

Simulation: foreach block of latent variables zb do

Draw a candidate $z_b^c\sim p_b\left(.|z_b^k\right)$.

Set $z^c=\left(z_1^{k\text{+1}},\dots ,z_{b\text{-1}}^{k\text{+1}},z_b^c,z_{b\text{+1}}^k,\dots ,z_{n_b}^k\right)$.

Compute the acceptation ratio $\omega =\text{min}\left[\text{1},\frac{q\left(z^c|y,{\theta }^k\right)}{q\left(z^k|y,{\theta }^k\right)}\right]$.

end

Stochastic approx.: $S^{k+1}\leftarrow S^k+{\rho }^k\left[S\left(Z^{k+1}\right)-S^k\right]$.

Maximization: ${\theta }^{k+1}\leftarrow \theta *\left(S^{k+1}\right)$.

Increment: set k ← k + 1.

until convergence;

output: Estimation of θ*.

Samples ($z^s$)s approximately distributed following q(z|y,θ∗).