sensitivity (version 1.16.2)

fast99: Extended Fourier Amplitude Sensitivity Test

Description

fast99 implements the so-called "extended-FAST" method (Saltelli et al. 1999). This method allows the estimation of first order and total Sobol' indices for all the factors (alltogether \(2p\) indices, where \(p\) is the number of factors) at a total cost of \(n \times p\) simulations.

Usage

fast99(model = NULL, factors, n, M = 4, omega = NULL,
       q = NULL, q.arg = NULL, …)
# S3 method for fast99
tell(x, y = NULL, …)
# S3 method for fast99
print(x, …)
# S3 method for fast99
plot(x, ylim = c(0, 1), …)

Arguments

model

a function, or a model with a predict method, defining the model to analyze.

factors

an integer giving the number of factors, or a vector of character strings giving their names.

n

an integer giving the sample size, i.e. the length of the discretization of the s-space (see Cukier et al.).

M

an integer specifying the interference parameter, i.e. the number of harmonics to sum in the Fourier series decomposition (see Cukier et al.).

omega

a vector giving the set of frequencies, one frequency for each factor (see details below).

q

a vector of quantile functions names corresponding to wanted factors distributions (see details below).

q.arg

a list of quantile functions parameters (see details below).

x

a list of class "fast99" storing the state of the sensitivity study (parameters, data, estimates).

y

a vector of model responses.

ylim

y-coordinate plotting limits.

…

any other arguments for model which are passed unchanged each time it is called.

Value

fast99 returns a list of class "fast99", containing all the input arguments detailed before, plus the following components:

call

the matched call.

X

a data.frame containing the factors sample values.

y

a vector of model responses.

V

the estimation of variance.

D1

the estimations of Variances of the Conditional Expectations (VCE) with respect to each factor.

Dt

the estimations of VCE with respect to each factor complementary set of factors ("all but \(X_i\)").

Details

If not given, the set of frequencies omega is taken from Saltelli et al. The first frequency of the vector omega is assigned to each factor \(X_i\) in turn (corresponding to the estimation of Sobol' indices \(S_i\) and \(S_{T_i}\)), other frequencies being assigned to the remaining factors.

If the arguments q and q.args are not given, the factors are taken uniformly distributed on \([0,1]\). The argument q must be list of character strings, giving the names of the quantile functions (one for each factor), such as qunif, qnorm… It can also be a single character string, meaning same distribution for all. The argument q.arg must be a list of lists, each one being additional parameters for the corresponding quantile function. For example, the parameters of the quantile function qunif could be list(min=1, max=2), giving an uniform distribution on \([1,2]\). If q is a single character string, then q.arg must be a single list (rather than a list of one list).

References

A. Saltelli, S. Tarantola and K. Chan, 1999, A quantitative, model independent method for global sensitivity analysis of model output, Technometrics, 41, 39--56.

R. I. Cukier, H. B. Levine and K. E. Schuler, 1978, Nonlinear sensitivity analysis of multiparameter model systems. J. Comput. Phys., 26, 1--42.

Examples

# NOT RUN {
# Test case : the non-monotonic Ishigami function
x <- fast99(model = ishigami.fun, factors = 3, n = 1000,
            q = "qunif", q.arg = list(min = -pi, max = pi))
print(x)
plot(x)
# }