To address the first question, I suggest you have a look at canonical correlation analysis and to a more recent dimension reduction technique called sliced inverse regression. On the latter, see the initial paper by Ker Chau Li

Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, 86(414):316–327, 1991.

It is freely available on the Internet. The version with the (interesting) comments you might have to buy thought.

Some important parameters for the choice of a method in you situation are :

• dimensionality of the input (n=3, n=15 and n=50 are very different problems);
• time needed to get one evaluation (0.1 s, 5 min and 5 hours are also very different problems);
• assumptions that you can make about your model : is it linear ? is it monotonous ?

Also you mention a possible multivariate output. If you have a few of them that represent completely different things, just do several independent sensitivity analysis.

If they are higly correlated or functional then it also change the problematic a lot.

You should make all this points clear before going for a given methodology.

To address the first question, I suggest you have a look at canonical correlation analysis and to a more recent dimension reduction technique called sliced inverse regression. On the latter, see the initial paper by Ker Chau Li

Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, 86(414):316–327, 1991.

It is freely available on the Internet. The version with the (interesting) comments you might have to buy thought.

Some important parameters for the choice of a method in you situation are :

• dimensionality of the input (n=3, n=15 and n=50 are very different problems);
• time needed to get one evaluation (0.1 s, 5 min and 5 hours are also very different problems);
• assumptions that you can make about your model : is it linear ? is it monotonous ?

Also you mention a possible multivariate output. If you have a few of them that represent completely different things, just do several independent sensitivity analysis.

If they are higly correlated or functional then it also change the problematic a lot.

You should make all this points clear before going for a given methodology.

To address the first question, I suggest you have a look at canonical correlation analysis and to a more recent dimension reduction technique called sliced inverse regression. On the latter, see the initial paper by Ker Chau Li : Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, 86(414):316–327, 1991.

It is freely available on the Internet. The version with the (interesting) comments you might have to buy thought.

Some important parameters for the choice of a method in you situation are :

• dimensionality of the input (n=3, n=15 and n=50 are very different problems);
• time needed to get one evaluation (0.1 s, 5 min and 5 hours are also very different problems);
• assumptions that you can make about your model : is it linear ? is it monotonous ?

Also you mention a possible multivariate output. If you have a few of them that represent completely different things, just do several independent sensitivity analysis.

If they are higly correlated or functional then it also change the problematic a lot.

You should make all this points clear before going for a given methodology.

To address the first question, I suggest you have a look at canonical correlation analysis and to a more recent dimension reduction technique called sliced inverse regression. On the latter, see the initial paper by Ker Chau Li

Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, 86(414):316–327, 1991.

It is freely available on the Internet. The version with the (interesting) comments you might have to buy thought.

Some important parameters for the choice of a method in you situation are :

• dimensionality of the input (n=3, n=15 and n=50 are very different problems);
• time needed to get one evaluation (0.1 s, 5 min and 5 hours are also very different problems);
• assumptions that you can make about your model : is it linear ? is it monotonous ?

Also you mention a possible multivariate output. If you have a few of them that represent completely different things, just do several independent sensitivity analysis.

If they are higly correlated or functional then it also change the problematic a lot.

You should make all this points clear before going for a given methodology.