Is delta output symmetric?

[jaimsierra]

Hi,

I'm using the Delta Moment-Independent Analysis with given data, checking a pair of variables at a time (a dependent one vs an independent one). Given this, and according to Plischke et al. (2013)**, who shows that delta is symmetric ( δ(Y,X) = δ(X,Y) ), I understood I should get same results for two combinations of, lets call them, var_a and var_b. I don't know if I am interpreting it well or not understanding anything, but trying to apply it I get significantly different results: δ(var_a,var_b)=0.313, δ(var_b,var_a)=0.703.

I am using the following function:
out=SALib.analyze.delta.analyze(problem,x,y,method='delta',conf_level=0.95,seed=92)

where x and y are both numpy.ndarray.

Do you have any idea why? Thanks for your help!

** Plischke, E., E. Borgonovo, and C. L. Smith (2013). “Global sensitivity measures from given data.” European Journal of Operational Research, 226(3):536-550, doi:10.1016/j.ejor.2012.11.047.

[ConnectedSystems]

Hello, thanks for the question @jaimsierra

Could you share what we call an MWE (Minimum Working Example)?

Some example code and data that we can use to reproduce the issue you're seeing?

It is hard to comment without being able to see exactly what you are doing.

That said:

I dont have access to the paper right now, but I wonder if X and Y are meant to be model inputs and outputs?

e.g., δ(Y, [var_a, var_b]) = δ([var_a, var_b], Y)

[jaimsierra]

Sure, thanks @ConnectedSystems:

##########################
#First check

y=df['var_a'].values
x=df['var_b'].values.reshape(-1, 1)

problem = {
    'num_vars': 1,
    'names': 'var_b',
               }

out1=SALib.analyze.delta.analyze(problem,x,y,method='delta',conf_level=0.95,seed=92)

print(out1)

##########################
#Second check

y=df['var_b'].values
x=df['var_a'].values.reshape(-1, 1)

problem = {
    'num_vars': 1,
    'names': 'var_a',
               }

out2=SALib.analyze.delta.analyze(problem,x,y,method='delta',conf_level=0.95,seed=92)

print(out2)```

[ConnectedSystems]

In this example are x and y variables to use as input to a model?
Or is only x an input, and y the model output?

Also, wrap your example with triple backticks (```) to format your code, like so:

```
some code
```

Otherwise it will not be formatted correctly

[jaimsierra]

Thanks @ConnectedSystems, changed!

In the example, x and y are variables to use as input to a model in a latter stage and, according to the property I was referring to, mutually exchangeable as inputs. I'm trying to use the property to find out the level of dependence between variables (as δ(X,Y)=0 means X and Y are independent).