Algorithm 1 Monte Carlo sampling for error propagation chain.

Calculation Step 1 for$k=1:N$do ${\overline{x}}_{\mathrm{sampled}}=\overline{x}+\overline{\sigma };R\sim \mathcal{N}(0,1)$ $\overline{y_k}=f({\overline{x}}_{\mathrm{sampled}},t,\theta )$ end for ${\overline{y}}_1=\frac{{\sum }_{k=1}^N{\overline{y}}_k}{N}$ ${\overline{\sigma }}_1=\sqrt{\frac{{\sum }_{k=1}^N({\overline{y}}_k-\overline{y}{)}^2}{N-1}}$ Calculation step i for$k=1:N$do ${\overline{y}}_{i,\mathrm{sampled}}={\overline{y}}_{i-1}+{\overline{\sigma }}_{i-1};R\sim \mathcal{N}(0,1)$ $\overline{y_k}=f({\overline{y}}_{i,\mathrm{sampled}},t,\theta )$ end for ${\overline{y}}_i=\frac{{\sum }_{k=1}^N{\overline{y}}_k}{N}$ ${\overline{\sigma }}_i=\sqrt{\frac{{\sum }_{k=1}^N({\overline{y}}_k-\overline{y}{)}^2}{N-1}}$