November 17th, 2015, 2:01 pm
A couple of random thoughts:1. A brute force method is to iterate using the standard method with post corrections: build your subjective matrix; find the nearest PSD correlation matrix; adjust any incorrectly changed correlations; find the nearest PSD correlation matrix; rinse & repeat. The amount of adjustment you do could be weighted by the confidence on the individual elements.2. Is there a way to change the construction process to start with the confidently known correlation values and then ask for estimates of less well known values within intervals computed to be safely PSD? Given a series of known correlation values, one can estimate a default chained correlation (Rij = f({Rik,Rkj})) and let the expert adjust it a bit up or down rather than let the expert enter a value that might be wildly inconsistent with PSD.3. One key invariant in PSD correlation matrices is that the total mass of negative correlations is strictly bounded as a function of the number of dimensions. That is, one cannot have that many large magnitude negative correlations in the matrix and still have PSD. Perhaps a quick-and-dirty sum-of-the-negative correlations would provide a warning that the experts are putting in too much negative correlation. The experts could then allocate negativity to avoid gross violations of PSD.