Dear San

As soon as you have data (even few points) you can easily compute the *Spearman rank correlation*, as easily as the Pearson linear correlation.

- you first compute the rank of each point in the sample set, i.e. its position in the sorted sample. For instance, if

\mathcal{X} = \{0.5 \quad 0.6 \quad 0.3 \quad 0.12 \quad 0.56 \quad 0.45 \quad 0.14 \quad 0.58 \quad 0.65 \quad 0.77 \}

then the ranks of the values are: r_{\mathcal X} = \{ 5 \; 8 \; 3 \; 1 \; 6 \; 4 \; 2 \; 7 \; 9 \; 10\}, that is 0.12 has rank 1 as it is the smallest value of the sample, whereas 0.65 has rank 9 since it is the second largest value.

- Once you have the ranks r_{{\mathcal X}_i} and r_{{\mathcal X}_j} of samples \mathcal{X}_i and \mathcal{X_j} (from two correlated parameters X_i and X_j), Spearman’s rank correlation is simply the
**linear** correlation between the ranks:

\rho_S(\mathcal{X}_i, \, \mathcal{X}_j) = \rho(r_{{\mathcal X}_i}, r_{{\mathcal X}_j}).

So why not do it and use the result to parametrize a Gaussian copula?

Best regards

Bruno