sensitivity (version 1.28.0)

sobolEff: Monte Carlo Estimation of Sobol' Indices (formulas of Janon-Monod)

Description

sobolEff implements the Monte Carlo estimation of the Sobol' sensitivity indices using the asymptotically efficient formulas in section 4.2.4.2 of Monod et al. (2006). Either all first-order indices or all total-effect indices are estimated at a cost of \(N \times (p+1)\) model calls or all closed second-order indices are estimated at a cost of \(N \times p \choose 2)\) model calls.

Usage

sobolEff(model = NULL, X1, X2, order=1, nboot = 0, conf = 0.95, ...)
# S3 method for sobolEff
tell(x, y = NULL, ...)
# S3 method for sobolEff
print(x, ...)
# S3 method for sobolEff
plot(x, ylim = c(0, 1), ...)
# S3 method for sobolEff
ggplot(x, ylim = c(0, 1), ...)

Value

sobolEff returns a list of class "sobolEff", 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

a vector of model responses.

S

the estimations of the Sobol' sensitivity indices.

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.

order

an integer specifying the indices to estimate: 0 for total effect indices,1 for first-order indices and 2 for closed second-order indices.

nboot

the number of bootstrap replicates, or zero to use asymptotic standard deviation estimates given in Janon et al. (2012).

conf

the confidence level for confidence intervals.

x

a list of class "sobolEff" 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.

Author

Alexandre Janon, Laurent Gilquin

Details

The estimator used by sobolEff is defined in Monod et al. (2006), Section 4.2.4.2 and studied under the name T_N in Janon et al. (2012). This estimator is good for large first-order indices.

References

Monod, H., Naud, C., Makowski, D. (2006), Uncertainty and sensitivity analysis for crop models in Working with Dynamic Crop Models: Evaluation, Analysis, Parameterization, and Applications, Elsevier.

A. Janon, T. Klein, A. Lagnoux, M. Nodet, C. Prieur (2014), Asymptotic normality and efficiency of two Sobol index estimators, ESAIM: Probability and Statistics, 18:342-364.

See Also

sobol, sobol2002, sobolSalt, sobol2007, soboljansen, sobolmartinez, sobolSmthSpl

Examples

# 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])
n <- 1000
X1 <- data.frame(matrix(runif(8 * n), nrow = n))
X2 <- data.frame(matrix(runif(8 * n), nrow = n))

# sensitivity analysis
x <- sobolEff(model = sobol.fun, X1 = X1, X2 = X2, nboot = 0)
print(x)

library(ggplot2)
ggplot(x)