Hi 👋

Thanks for the question.

When you define your problem, you can define any distribution you want for the parameters. Then it will work just fine (and is also correct from a statistical standpoint.)

You can use your own sample to pass to the analysis part. But you must use the correct matrix format with A, B, AB, BA. So I would not recommend doing it. Missing a single point would make the analysis wrong.

We had plans for deprecating the Saltelli method.

What we can do is to go forward but also propose a new generic API that would basically be the new Sobol' but with a sampling method parameter.

Hi
Thanks for the response.
What do you mean by 'use the correct matrix format with A, B, AB, BA'?

I mean that the analysis function expects to be constructed in a very specific way. It's not just a list of samples. First it takes two independent samples: A, B. Then it makes a matrix AB (and BA if second order) by mixing A and B. And it then interleaves the matrices together. So when the analysis gets the input sample, it decomposes it into these matrices and if one point is out of place, it will not work and results will be random.

In the case of only two parameters (i.e., no second order), isn't it enough if Y.size is divisible by (D 2) [which is 4 in our case]?

Doesn't this take care of the matrices?

Sorry I don't understand your question.

In case of 2 parameters, you would only have A, B and AB. But it's not just about being divisible. As you can see in the code, the input sample Y is decomposed into A, B, AB in a specific order. A, AB, B, A, AB, B, etc. And Y was constructed by scrambling the inputs that way.

You cannot take an existing random sample and split it in 3 to get A, B and AB. You must start with 2 matrices in your parameter space: A, B. Then AB is (for 2 parameters–don't quote me on the order, just to show it's not that straightforward): [A[:, 0], B[:, 1], A[:, 1], B[:, 0]]. Then you use this sample with your model to get f_A, f_B, f_AB. And the concatenation of these 3 gives you Y.

Correct me if I am wrong, but I see that Y is the model output array. And the code splits the output array into A, B, AB matrices.
Y is evaluated initially over the total sample space, and later, inside the function sobol.analyze, the matrices are formed.

Ref:

The matrices are not formed in sobol.analyze but "retrieved".

Y is the model output array and X is the sample leading to Y: f(X) -> Y

saltelli.sample (or sobol.sample) is creating X in a very specific way as I explained. saltelli.sample makes at least three matrices A, B, AB and concatenate them together to give X.

There is of course a direct relationship between samples in X and model outputs in Y.

All that to say that you cannot take an arbitrary sample X (from a random sampling for instance) and then get Y and pass it to sobol.analyze. This is incorrect. If you want to construct yourself X, you must follow the rules I outlined above (A, B, AB with the correct column re-ordering to get AB.)

Thank you for your time! Appreciate it!

Of course, glad I could help.

I am re-opening since there is a possible enhancement with the addition of a method parameter in saltelli.sample (or the function that would supersede it.)