sobol2007 | R Documentation |
sobol2007
implements the Monte Carlo estimation of
the Sobol' indices for both first-order and total indices at the same
time (alltogether 2p
indices), at a total cost of (p+2)
\times n
model evaluations. These are called the Mauntz estimators.
sobol2007(model = NULL, X1, X2, nboot = 0, conf = 0.95, ...)
## S3 method for class 'sobol2007'
tell(x, y = NULL, return.var = NULL, ...)
## S3 method for class 'sobol2007'
print(x, ...)
## S3 method for class 'sobol2007'
plot(x, ylim = c(0, 1), ...)
## S3 method for class 'sobol2007'
plotMultOut(x, ylim = c(0, 1), ...)
## S3 method for class 'sobol2007'
ggplot(data, mapping = aes(), ylim = c(0, 1), ..., environment
= parent.frame())
model |
a function, or a model with a |
X1 |
the first random sample. |
X2 |
the second random sample. |
nboot |
the number of bootstrap replicates. |
conf |
the confidence level for bootstrap confidence intervals. |
x |
a list of class |
data |
a list of class |
y |
a vector of model responses. |
return.var |
a vector of character strings giving further
internal variables names to store in the output object |
ylim |
y-coordinate plotting limits. |
mapping |
Default list of aesthetic mappings to use for plot. If not specified, must be supplied in each layer added to the plot. |
environment |
[Deprecated] Used prior to tidy evaluation. |
... |
any other arguments for |
This estimator is good for small first-order and total indices.
BE CAREFUL! This estimator suffers from a conditioning problem when estimating
the variances behind the indices computations. This can seriously affect the
Sobol' indices estimates in case of largely non-centered output. To avoid this
effect, you have to center the model output before applying "sobol2007"
.
Functions "sobolEff"
, "soboljansen"
and "sobolmartinez"
do not suffer from this problem.
sobol2007
returns a list of class "sobol2007"
, containing all
the input arguments detailed before, plus the following components:
call |
the matched call. |
X |
a |
y |
the response used |
V |
the estimations of Variances of the Conditional Expectations
(VCE) with respect to each factor and also with respect to the
complementary set of each factor ("all but |
S |
the estimations of the Sobol' first-order indices. |
T |
the estimations of the Sobol' total sensitivity indices. |
Users can ask more ouput variables with the argument
return.var
(for example, bootstrap outputs V.boot
,
S.boot
and T.boot
).
Bertrand Iooss
I.M. Sobol, S. Tarantola, D. Gatelli, S.S. Kucherenko and W. Mauntz, 2007, Estimating the approximation errors when fixing unessential factors in global sensitivity analysis, Reliability Engineering and System Safety, 92, 957–960.
A. Saltelli, P. Annoni, I. Azzini, F. Campolongo, M. Ratto and S. Tarantola, 2010, Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index, Computer Physics Communications 181, 259–270.
sobol, sobol2002, sobolSalt, soboljansen, sobolmartinez, sobolEff, sobolmara, sobolMultOut
# Test case : the non-monotonic Sobol g-function
# The method of sobol requires 2 samples
# There are 8 factors, all following the uniform distribution
# on [0,1]
library(boot)
n <- 1000
X1 <- data.frame(matrix(runif(8 * n), nrow = n))
X2 <- data.frame(matrix(runif(8 * n), nrow = n))
# sensitivity analysis
x <- sobol2007(model = sobol.fun, X1, X2, nboot = 100)
print(x)
plot(x)
library(ggplot2)
ggplot(x)
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