R: Monte Carlo Estimation of Sobol' Indices (improved formulas...
sobolowen
R Documentation
Monte Carlo Estimation of Sobol' Indices (improved formulas of Owen (2013)
Description
sobolowen implements the Monte Carlo estimation of
the Sobol' indices for both first-order and total indices at the same
time (alltogether 2p indices). Take as input 3 independent matrices.
These are called the Owen estimators.
Usage
sobolowen(model = NULL, X1, X2, X3, nboot = 0, conf = 0.95, varest = 2, ...)
## S3 method for class 'sobolowen'
tell(x, y = NULL, return.var = NULL, varest = 2, ...)
## S3 method for class 'sobolowen'
print(x, ...)
## S3 method for class 'sobolowen'
plot(x, ylim = c(0, 1), ...)
Arguments
model
a function, or a model with a predict method,
defining the model to analyze.
X1
the first random sample.
X2
the second random sample.
X3
the third random sample.
nboot
the number of bootstrap replicates.
conf
the confidence level for bootstrap confidence intervals.
varest
choice for the variance estimator for the denominator of
the Sobol' indices. varest=1 is for a classical estimator.
varest=2 (default) is for the estimator proposed in Janon et al. (2012).
x
a list of class "sobol" storing the state of the
sensitivity study (parameters, data, estimates).
y
a vector of model responses.
return.var
a vector of character strings giving further
internal variables names to store in the output object x.
ylim
y-coordinate plotting limits.
...
any other arguments for model which are passed
unchanged each time it is called
Value
sobolowen returns a list of class "sobolowen", containing all
the input arguments detailed before, plus the following components:
call
the matched call.
X
a data.frame containing the design of experiments.
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 Xi").
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).
Author(s)
Taieb Touati and Bernardo Ramos
References
A. Owen, 2013, Better estimations of small Sobol' sensitivity indices,
ACM Transactions on Modeling and Computer Simulations (TOMACS), 23(2), 11.
Janon, A., Klein T., Lagnoux A., Nodet M., Prieur C. (2012), Asymptotic
normality and efficiency of two Sobol index estimators. Accepted in
ESAIM: Probability and Statistics.