sobolrank {sensitivity}

First-order sensitivity indices estimation via ranking

Description

sobolrank implements the estimation of all first-order indices using only N model evaluations via ranking following Gamboa et al. (2020) and inspired by Chatterjee (2019).

Usage

sobolrank(model = NULL, X, nboot = 0, conf = 0.95, nsample = round(0.8*nrow(X)), ...)
## S3 method for class 'sobolrank'
tell(x, y = NULL, ...)
## S3 method for class 'sobolrank'
print(x, ...)
## S3 method for class 'sobolrank'
plot(x, ylim = c(0, 1), ...)
## S3 method for class 'sobolrank'
ggplot(data, mapping = aes(), ..., environment
                 = parent.frame(), ylim = c(0, 1))

Arguments

model

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

X

a random sample of the inputs.

nboot

the number of bootstrap replicates, see details.

conf

the confidence level for confidence intervals, see details.

nsample

the size of the bootstrap sample, see details.

x

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

data

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

y

a vector of model responses.

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

The estimator used by sobolrank is defined in Gamboa et al. (2020). It is based on ranking the inputs as was first proposed by Chatterjee (2019) for a Cramer-Von Mises based estimator. All first-order indices can be estimated with a single sample of size N. Since boostrap creates ties which are not accounted for in the algorithm, confidence intervals are obtained by sampling without replacement with a sample size nsample.

Value

sobolrank returns a list of class "sobolrank", 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.

Author(s)

Sebastien Da Veiga

References

Gamboa, F., Gremaud, P., Klein, T., & Lagnoux, A., 2022, Global Sensitivity Analysis: a novel generation of mighty estimators based on rank statistics, Bernoulli 28: 2345-2374.

Chatterjee, S., 2021, A new coefficient of correlation, Journal of the American Statistical Association, 116:2009-2022.

See Also

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

Examples

# Test case : the non-monotonic Sobol g-function
# Example with a call to a numerical model
library(boot)
n <- 1000
X <- data.frame(matrix(runif(8 * n), nrow = n))
x <- sobolrank(model = sobol.fun, X = X, nboot = 100)
print(x)
library(ggplot2)
ggplot(x)
# Test case : the Ishigami function
# Example with given data
n <- 500
X <- data.frame(matrix(-pi+2*pi*runif(3 * n), nrow = n))
Y <- ishigami.fun(X)
x <- sobolrank(model = NULL, X)
tell(x,Y)
print(x)
ggplot(x)