OakleyOHaganSensitivity¶
- class OakleyOHaganSensitivity¶
Class to define a Oakley-O’Hagan sensitivity benchmark problem.
Methods
Returns the first order Sobol' sensitivity indices.
Returns the function.
Returns the input distribution.
getName
()Returns the name of the problem.
Returns the total order Sobol' sensitivity indices.
- __init__()¶
Create a Oakley-O’Hagan sensitivity problem.
The function is defined by the equation:
where
The input random variables are independent.
Notes
The dimension and parameters of this problem cannot be changed. The Sobol’ sensitivity indices are estimate with as much accuracy as possible.
The model was first introduced in (Oakley, O’Hagan, 2004).
The reference Sobol’ indices were computed from a sparse polynomial chaos. A Sobol’ low discrepancy design of experiments was generated with 500 training points. The sparse polynomial chaos expansion used an hyperbolic enumeration rule and a polynomial degree 6. The coefficients were estimated from regression. With 500 points in the validation set, the Q2 was greater than 98%. There are 2 significant digits in the reference results.
References
Oakley, J. E., & O’Hagan, A. (2004). Probabilistic sensitivity analysis of complex models: a Bayesian approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(3), 751-769.
Derek Bingham, https://www.sfu.ca/~ssurjano/oakoh04.html
Examples
>>> import otbenchmark as otb problem = OakleyOHaganSensitivity()
- getFirstOrderIndices()¶
Returns the first order Sobol’ sensitivity indices.
- Parameters:
- None.
- Returns:
- firstOrderIndices: ot.Point
The first order sensitivity indices.
- getFunction()¶
Returns the function.
- Parameters:
- None.
- Returns:
- function: ot.Function
The function.
- getInputDistribution()¶
Returns the input distribution.
- Parameters:
- None.
- Returns:
- distribution: ot.Distribution
The distribution.
- getName()¶
Returns the name of the problem.
- Parameters:
- None.
- Returns:
- name: str
The name.
- getTotalOrderIndices()¶
Returns the total order Sobol’ sensitivity indices.
- Parameters:
- None.
- Returns:
- totalOrderIndices: ot.Point
The total order sensitivity indices.