Hello!
I am a beginner at building metamodels and I have two theoretical questions about the process.
- I have a question in regards to building the polynomial basis and calculation of the coefficients of PCE models. I can’t seem to understand how are the moment (parameters) of the marginal pdfs of the variables used in it. So if I have an experimental data set and I specify the marginals for the input variables:
Input.Marginals(1).Type = ‘Gaussian’;
Input.Marginals(1).Parameters = [0 1];
Input.Marginals(2).Type = ‘Gaussian’;
Input.Marginals(2).Moments = [0 1];
and than also choose the polynomials in regards to the marginals pdfs:
MetaOpts.PolyTypes = {‘hermite’,‘hermite’};
and the maximal degree of the basis:
MetaOpts.Degree = 2;
while I am using the ‘OLS’ method for the calculation of the coefficients, how are the parameters of the marginal distributions used? I have chosen the polynomials and the maximal degree of the basis (so I already know the basis) and I get the coefficients with the OLS method directly from evaluating on the experimental data set, so how do the parameters influence the PCE model/bases?
- The second question is in regards to copulas. So if I have the same input for example, how will using a Gaussian copula mathematically influence the basis?
InputOpts.Copula.Type = ‘Gaussian’;
InputOpts.Copula.RankCorr = [1 0.8; 0.8 1];
So where in the calculation does the copula change the model? The polynomials in the basis? The coefficients?
I would really appreciate the help.
Thanks