# [ot-users] Point in standard space and importance factors

Anita Laera anita.laera87 at gmail.com
Wed Apr 5 11:55:06 CEST 2017

```Dear all,
I wanted to calculate the importance factors at the end of a Monte Carlo
analysis without using the function getImportanceFactors(), in order to
validate the results. I am performing the following steps:

-          Get the mean point in the event domain,

-          Transform the point in the standard space

-          Calculate the importance factors.

I start from the same mean point in the event domain, but the results I get
through openturns (getImportanceFactors()) and my script are different.

In particular, if I input the same point in terms of standard space
coordinates in the function that calculates the importance factors, the
results are identical. This means that I might have an error in the
transformation in the standard space.

I couldn’t find a lot of information about it, so this is what I am doing.

point is a list of floats representing the mean point in event domain ([xp_1,
xp_2, …, xp_n]).

variables_values is a list of lists. The length of variables_values is
equal to the number of iterations. The length of each sub-list is equal to
the number of random variables ([[x'_1, x'_2, …, x'_n], [x''_1, x''_2, …,
x''_n], [x'''_1, x'''_2, …, x'''_n], …]).

For each random variable x_i, I calculate the mean (mean_i) and the
standard deviation (std_i) (based on the values in variable_values
corresponding to x_i).

The value of the design point in the standard space at the i-th position is
calculated as:

point_in_standard_space[i] = (point[i] – mean_i) / std_i = (xp_i - mean_i)
/ std_i

When I input the point calculated in this way, the resulting importance
factors are a bit different in the case of a Monte Carlo analysis. In the
case of Monte Carlo I can’t get the transformed mean point in event domain
in the standard space, since I didn’t find a built-in function for that in
openturns.

In the case of a FORM analysis, I have very different results. In that case
I can compare my transformed design point with the standard space design
point calculated by openturns but they are very different. I am not sure
if, in the case of FORM, variables_values should contain only the values of
x_i at each iteration or also at each function evaluation. I have
considered both cases and I couldn’t get the same results as openturns.

When I use the transformed point in the standard space given by openturns,
the importance factors are the same. Also in this case, I am sure that
something goes wrong when transforming the point in the standard space.