sobol2002: Monte Carlo Estimation of Sobol' Indices (scheme by Saltelli 2002)

Description

sobol2002 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 Saltelli estimators.

Usage

sobol2002(model = NULL, X1, X2, nboot = 0, conf = 0.95, ...)
## S3 method for class 'sobol2002':
tell(x, y = NULL, return.var = NULL, \dots)
## S3 method for class 'sobol2002':
print(x, \dots)
## S3 method for class 'sobol2002':
plot(x, ylim = c(0, 1), ...)

Arguments

model

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

the first random sample.

the second random sample.

nboot

the number of bootstrap replicates.

conf

the confidence level for bootstrap confidence intervals.

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

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

sobol2002 returns a list of class "sobol2002", containing all the input arguments detailed before, plus the following components:
callthe matched call.
Xa data.frame containing the design of experiments.
ythe response used
Vthe 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 $X_i$").
Sthe estimations of the Sobol' first-order indices.
Tthe 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).

Details

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 "sobol2002". Functions "sobolEff", "soboljansen" and "sobolmartinez" do not suffer from this problem.

References

A. Saltelli, 2002, Making best use of model evaluations to compute sensitivity indices, Computer Physics Communication, 145, 580--297.

Examples

Run this code

# 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 <- sobol2002(model = sobol.fun, X1, X2, nboot = 100)
print(x)
plot(x)

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