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

In sensitivity: Global Sensitivity Analysis of Model Outputs

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, ...)
## S3 method for class 'sobol2002'
print(x, ...)
## S3 method for class 'sobol2002'
plot(x, ylim = c(0, 1), ...)
  ## S3 method for class 'sobol2002'
plotMultOut(x, ylim = c(0, 1), ...)
## S3 method for class 'sobol2002'
ggplot(data, mapping = aes(), ylim = c(0, 1), ..., environment
                 = parent.frame())

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.
nboot	the number of bootstrap replicates.
conf	the confidence level for bootstrap confidence intervals.
x	a list of class "sobol2002" storing the state of the sensitivity study (parameters, data, estimates).
data	a list of class "sobol2002" 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.
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 model which are passed unchanged each time it is called

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.

Value

sobol2002 returns a list of class "sobol2002", 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 X_i").
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)

Gilles Pujol

References

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

See Also

sobol, sobolSalt, sobol2007, soboljansen, sobolmartinez, sobolEff, sobolmara, sobolGP,sobolMultOut

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]

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)

library(ggplot2)
ggplot(x)

sensitivity documentation built on Aug. 31, 2023, 5:10 p.m.