sensitivity (version 1.16.2)

sobolSalt: Monte Carlo Estimation of Sobol' Indices based on Saltelli schemes

Description

sobolSalt implements the Monte Carlo estimation of the Sobol' indices for either both first-order and total effect indices at the same time (alltogether \(2p\) indices) at a total cost of \(n\times(p+2)\) model evaluations; or first-order, second-order and total indices at the same time (alltogether \(2p+ p\times(p-1)/2\) indices) at a total cost of \(n\times(2\times p+2)\) model evaluations.

Usage

sobolSalt(model = NULL, X1, X2, scheme="A", nboot = 0, conf = 0.95, …)
# S3 method for sobolSalt
tell(x, y = NULL, …)
# S3 method for sobolSalt
print(x, …)
# S3 method for sobolSalt
plot(x, ylim = c(0, 1), choice, …)
# S3 method for sobolSalt
ggplot(x, ylim = c(0, 1), choice, …)

Arguments

model

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

X1

the first random sample (containing n points).

X2

the second random sample (containing n points).

scheme

a letter "A" or "B" indicating which scheme to use (see "Details")

nboot

the number of bootstrap replicates.

conf

the confidence level for bootstrap confidence intervals.

x

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

y

a vector of model responses.

ylim

y-coordinate plotting limits.

choice

an integer specifying which indices to plot: 1 for first-order and total effect indices, 2 for second-order indices.

…

any other arguments for model which are passed unchanged each time it is called

Value

sobolSalt returns a list of class "sobolSalt", 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 model variance.

S

the estimations of the Sobol' first-order indices.

S2

the estimations of the Sobol' second-order indices (only for scheme "B").

T

the estimations of the Sobol' total sensitivity indices.

Details

The estimators used are the one implemented in "sobolEff".

scheme specifies which Saltelli's scheme is to be used: "A" to estimate both first-order and total effect indices, "B" to estimate first-order, second-order and total effect indices.

References

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.

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

See Also

sobol, sobol2007, soboljansen, sobolmartinez, sobolEff

Examples

# NOT RUN {
# 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 <- sobolSalt(model = sobol.fun, X1, X2, scheme="A", nboot = 100)
print(x)
plot(x, choice=1)

library(ggplot2)
ggplot(x, choice=1)
# }