sobolrec implements a recursive version of the procedure introduced by Tissot & Prieur (2015) using two replicated nested designs. This function estimates either all first-order indices or all closed second-order indices at a total cost of 2*N model evaluations where N is the size of each replicated nested design.

sobolrec is located in package sensitivity. Please install and load package sensitivity before use.

sobolrec(model=NULL, factors, layers, order, precision, method=NULL, tail=TRUE, ...)
## S3 method for class 'sobolrec'
ask(x, index, ...)
## S3 method for class 'sobolrec'
tell(x, y = NULL, index, ...)
## S3 method for class 'sobolrec'
print(x, ...)
## S3 method for class 'sobolrec'
plot(x, ylim = c(0,1), ...)

install.packages("sensitivity", repo="http://cran.r-project.org", dep=T)
library(sensitivity)
## 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])

# first-order indices estimation
x <- sobolrec(model = sobol.fun, factors = 8, layers=rep(2,each=15), order=1,
precision = c(5*10^(-2),2), method=NULL, tail=TRUE)
print(x)

# closed second-order indices estimation
x <- sobolrec(model = sobol.fun, factors = 8, layers=11^2, order=2,
precision = c(10^(-2),3), method="al", tail=TRUE)
print(x)

# Test case: dealing with external model

x <- sobolrec(model = NULL, factors = 8, layers=rep(2,each=15), order=1,
precision = c(5*10^(-2),2), method=NULL, tail=TRUE)
toy <- sobol.fun
k <- 1
stop_crit <- FALSE
while(!(stop_crit) & (k<length(x$layers))){
ask(x, index=k)
y <- toy(x$block)
tell(x, y, index=k)
stop_crit <- x$stop_crit
k <- k+1
}
print(x)

## End(Not run)

Return Values: sobolrec returns a list of class "sobolrec", containing all the input arguments detailed before, plus the following components:

Details: For first-order indices, layers is a vector:

(s_1, ..., s_m)

specifying the number m of layers of the nested design whose respective size are given by:

s_1 * s_2 * ... * s_{k-1}, for k=2, ...,m+1.

For closed second-order indices, layers directly specifies the size of all layers.

For each Sobol' index S the stopping criterion writes:

| S_{l-1}-S_{l} | < ε

This criterion is tested for the last l_0 steps (including the current one). ε and l_0 are respectively the target precision and the number of steps of the stopping criterion specified in precision.

sobolrec uses either an algebraic or an accept-rejet method to construct the orthogonal arrays for the estimation of closed second-order indices. The algebraic method is less precise than the accept-reject method but offers more steps when the number of factors is small.

sobolrec automatically assigns a uniform distribution on [0,1] to each input. Transformations of distributions (between U[0,1] and the wanted distribution) have to be performed before the call to tell().

Warning messages:

"The value entered for layers is not the square of a prime number. It has been replaced by: "

When order=2, the value of layers must be the square of a prime power number. This warning message indicates that it was not the case and the value has been replaced depending on tail. If tail=TRUE (resp. tail=FALSE) the new value of layers is equal to the square of the prime number preceding (resp. following) the square root of layers.

"The value entered for layers is not satisfying the constraint. It has been replaced by: "

the value N for layers must satisfied the constraint N ≥ (d-1)^2 where d is the number of factors. This warning message indicates that N was replaced by the square of the prime number following (or equals to) d-1.