FAST and EFAST Methods
The Fourier Amplitude Sensitivity Test (FAST) is a method of sensitivity analysis, and works for monotonic and non-monotonic models alike, see references [14] and [15]. This method is based on performing numerical calculations to obtain the expected value and variance of a model prediction. The basis of this calculation is a transformation that converts a multidimensional integral over all the uncertain model inputs to a one-dimensional integral. Specifically, a search curve, which scans the whole parameter space, is constructed in order to avoid the multidimensional integration. A decomposition of the Fourier series representation is used to obtain the fractional contribution of the individual input variables to the variance of the model prediction.
The analysis is divided into four steps:
- construction of ranges and distributions for the xj and development of the expected value and variance of y formally in terms of integrals defined on the input parameter space Ω ;
- transformation of the multidimensional integral defined on Ω to a one-dimensional integral;
- estimation of expected value and variance for y;
- estimation of the sensitivity indices.
The
FAST sensitivity indices of the first order are calculated using the
terms in the
Fourier decomposition of the model output.
An
extension of FAST [14] can give, for the
same set of model evaluations (i.e. at no extra computational cost)
both the
first order sensitivity indices and the total ones.
The classical FAST method estimates the first order effects. The extension of FAST computes first order effects and total effects. This technique can also be used by grouping sub-sets of factors together.
IMPORTANT: The Fast method can be used with a set of uncorrelated factors whose cardinality is greater than one.