Algorithm 2 Generating parameter replicas $\tilde{\theta }$ from non independent samples.
(For the given sample $\{x_1,\dots ,x_m\}$ and well behaving statistic s)
• For d ranging in the inspection set 1. draw the forced seed ${\breve{\mathbf{u}}}_d=\{{\breve{u}}_1^d,\dots ,{\breve{u}}_m^d\}$ 2. get ${\theta }^{\ast }$ by solving in $\theta$ the master equation $$s=s(x_1,\dots ,x_m)=h(\theta ,{\breve{u}}_1^d,\dots ,{\breve{u}}_1^d)$$ (7) 3. store $\mathit{par}\left(d\right)={\theta }^{\ast }$ 4. compute the loss function $L\left(d\right)$ •get $\breve{\theta }=\mathit{par}(d^{\prime }=\mathit{argminL}(d\left)\right)$