fast {sensitivity} | R Documentation |
fast
is the implementation of the Fourier Amplitude Sensitivity
Test. This function computes the following non-linear indices of
sensitivity: first-order indices and total indices.
fast(model = NULL, factors, n, M = 4, G = "uniform", min = 0, max = 1, omega = NULL, ...) ## S3 method for class 'fast': compute(sa, y = NULL)
model |
the model. |
factors |
the number of factors, or their names. |
n |
the length of the discretization of the s-space. |
M |
the number of harmonics to sum. |
G |
the space transformation. |
min |
the minimum values for the factors (uniform distribution). |
max |
the maximum values for the factors (uniform distribution). |
omega |
the set of frequencies. |
sa |
the sensitivity analysis object. |
y |
the response. |
... |
any other arguments for model which are passed
unchanged each time it is called. |
model
is a function or a predictor (a class with a
predict
method) computing the response y
based on the
sample given by x
. If no model is specified, the indices will be
computed when one gives the response.
The space transformation G
is the function such that:
x_i = G_i( sin( omega_i * s ) )
It must be a function of two parameters (G <- function(i, x)
...
). If the string "uniform"
is given, then the function is
the best one for uniform factors on the range [a_i,
b_i]:
G_i(x) = a_i + (b_i - a_i) * ( 1/2 + 1/pi * asin(x) )
where a_i and b_i are the boundaries given by
the arguments min
and max
. min
and max
can
be single values (the same for each factor) or vectors.
If the set of frequencies omega
is not given, the function use
the set recommended by Saltelli (the so-called extended-FAST). The
first frequency is the greater, corresponding to the index of
interest, and the other correspond to the complementary set.
fast
returns an object of class "fast"
.
An object of class "fast"
is a list containing the following
components:
model |
the model. |
M |
the number of harmonics to sum. |
s |
the discretisation of the s-space. |
omega |
the set of frequencies. |
x |
the factor sample. |
y |
the response. |
S |
the estimations of the first-order indices. |
St |
the estimations of the total indices. |
call |
the matched call. |
Saltelli, A., Tarantola, S. and Chan, K., 1999, A quantitative, model independent method for global sensitivity analysis of model output. Technometrics, 41, 39–56.
Saltelli, A., Chan, K. and Scott, E. M., 2000, Sensitivity analysis. Wiley.
Cukier, R. I., Levine, H. B. and Schuler, K. E., 1978, Nonlinear sensitivity analysis of multiparameter model systems. J. Comput. Phys., 26, 1–42.
# Test case : the non-monotonic Sobol g-function sa <- fast(model = sobol.fun, factors = 8, n = 1000) print(sa) plot(sa)