Example: OHagan-function¶
This example deals with the surrogate modeling of O’Hagan function with 15 parameters. You will see how to check the quality of your regression model and perform sensitivity analysis via Sobol Indices
Oakley & O’Hagan (2004) Function
This function’s a-coefficients are chosen so that 5 of the input variables contribute significantly to the output variance, 5 have a much smaller effect, and the remaining 5 have almost no effect on the output variance.
O’Hagan, 2004, Probabilistic sensitivity analysis of complex models: a Bayesian approach J. R. Statist. Soc. B (2004) 66, Part 3, pp. 751-769.
This example trains a surrogate with AL. FastARD is set as the regression type and the space-filling sequential exploitaiton scheme is chosen as no data is given.
Model and Data¶
Property |
Setting |
|---|---|
Model type |
Function |
Number of input parameters |
15 |
Number of output parameters |
1 |
Time- or space- dependency |
?? |
MC reference |
No |
Parameter |
Distribution |
|---|---|
0-14 |
gaussian |
Surrogate¶
Property |
Setting |
|---|---|
surrogate-type |
aPCE |
associated model |
‘OHagan’ |
degree choices |
max degree 7, q-norm truncation 0.65 |
regression |
FastARD |
Property |
Setting |
|---|---|
Static sampling method |
latin-hypercube |
Number of static samples |
100 |
Number of total samples |
500 |
Number of samples per AL iteration |
1 |
AL tradeoff scheme |
None |
AL exploration method |
latin-hypercube, n_candidates=10000, n_cand_groups=4 |
AL exploitation method |
space-filling |