sobolGP | R Documentation |
Perform a kriging-based global sensitivity analysis taking into account both the meta-model and the Monte-Carlo errors. The Sobol indices are estimated with a Monte-Carlo integration and the true function is substituted by a kriging model. It is built thanks to the function km
of the package DiceKriging
.
The complete conditional predictive distribution of the kriging model is considered (not only the predictive mean).
sobolGP(
model,
type="SK",
MCmethod="sobol",
X1,
X2,
nsim=100,
nboot=1,
conf = 0.95,
sequential = FALSE,
candidate,
sequential.tot=FALSE,
max_iter = 1000)
## S3 method for class 'sobolGP'
ask(x, tot = FALSE, ...)
## S3 method for class 'sobolGP'
tell(x, y=NULL, xpoint=NULL, newcandidate=NULL, ...)
## S3 method for class 'sobolGP'
print(x, ...)
## S3 method for class 'sobolGP'
plot(x,...)
model |
an object of class |
type |
a character string giving the type of the considered kriging model. |
MCmethod |
a character string specifying the Monte-Carlo procedure used to estimate the Sobol indices. The avaible methods are : |
X1 |
a matrix representing the first random sample. |
X2 |
a matrix representing the second random sample. |
nsim |
an integer giving the number of samples for the conditional Gaussian process. It is used to quantify the uncertainty due to the kriging approximation. |
nboot |
an integer representing the number of bootstrap replicates. It is used to quantify the uncertainty due to the Monte-Carlo integrations. We recommend to set |
conf |
a numeric representing the confidence intervals taking into account the uncertainty due to the bootstrap procedure and the Gaussian process samples. |
sequential |
a boolean. If |
candidate |
a matrix representing the candidate points where the best new point to be simulated is selected. The lines represent the points and the columns represent the dimension. |
sequential.tot |
a boolean. If |
max_iter |
a numeric giving the maximal number of iterations for the propagative Gibbs sampler. It is used to simulate the realizations of the Gaussian process. |
x |
an object of class S3 |
tot |
a boolean. If |
xpoint |
a matrix representing a new point added to the kriging model. |
y |
a numeric giving the response of the function at |
newcandidate |
a matrix representing the new candidate points where the best point to be simulated is selected. If |
... |
any other arguments to be passed |
The function ask
provides the new point where the function should be simulated. Furthermore, the function tell
performs a new kriging-based sensitivity analysis when the point x
with the corresponding observation y
is added.
An object of class S3 sobolGP
.
call : a list containing the arguments of the function sobolGP
:
X1 : X1
X2 : X2
conf : conf
nboot : nboot
candidate : candidate
sequential : sequential
max_iter : max_iter
sequential.tot : sequential.tot
model : model
tot : tot
method : MCmethod
type : type
nsim : nsim
S : a list containing the results of the kriging-based sensitivity analysis for the MAIN effects:
mean : a matrix giving the mean of the Sobol index estimates.
var : a matrix giving the variance of the Sobol index estimates.
ci : a matrix giving the confidence intervals of the Sobol index estimates according to conf
.
varPG : a matrix giving the variance of the Sobol index estimates due to the Gaussian process approximation.
varMC : a matrix giving the variance of the Sobol index estimates due to the Monte-Carlo integrations.
xnew : if sequential=TRUE
, a matrix giving the point in candidate
which is the best to simulate.
xnewi : if sequential=TRUE
, an integer giving the index of the point in candidate
which is the best to simulate.
T : a list containing the results of the kriging-based sensitivity analysis for the TOTAL effects:
mean : a matrix giving the mean of the Sobol index estimates.
var : a matrix giving the variance of the Sobol index estimates.
ci : a matrix giving the confidence intervals of the Sobol index estimates according to conf
.
varPG : a matrix giving the variance of the Sobol index estimates due to the Gaussian process approximation.
varMC : a matrix giving the variance of the Sobol index estimates due to the Monte-Carlo integrations.
xnew : if sequential.tot=TRUE
, a matrix giving the point in candidate
which is the best to simulate.
xnewi : if sequential.tot=TRUE
, an integer giving the index of the point in candidate
which is the best to simulate.
Loic Le Gratiet, EDF R&D
L. Le Gratiet, C. Cannamela and B. Iooss (2014), A Bayesian approach for global sensitivity analysis of (multifidelity) computer codes, SIAM/ASA J. Uncertainty Quantification 2-1, pp. 336-363.
sobol
, sobol2002
, sobol2007
, sobolEff
, soboljansen
, sobolMultOut, km
library(DiceKriging)
#--------------------------------------#
# kriging model building
#--------------------------------------#
d <- 2; n <- 16
design.fact <- expand.grid(x1=seq(0,1,length=4), x2=seq(0,1,length=4))
y <- apply(design.fact, 1, branin)
m <- km(design=design.fact, response=y)
#--------------------------------------#
# sobol samples & candidate points
#--------------------------------------#
n <- 1000
X1 <- data.frame(matrix(runif(d * n), nrow = n))
X2 <- data.frame(matrix(runif(d * n), nrow = n))
candidate <- data.frame(matrix(runif(d * 100), nrow = 100))
#--------------------------------------#
# Kriging-based Sobol
#--------------------------------------#
nsim <- 10 # put nsim <- 100
nboot <- 10 # put nboot <- 100
res <- sobolGP(
model = m,
type="UK",
MCmethod="sobol",
X1,
X2,
nsim = nsim,
conf = 0.95,
nboot = nboot,
sequential = TRUE,
candidate,
sequential.tot=FALSE,
max_iter = 1000
)
res
plot(res)
x <- ask(res)
y <- branin(x)
# The following line doesn't work (uncorrected bug:
# unused argument in km(), passed by update(), eval(), tell.sobolGP() ??)
#res.new <- tell(res,y,x)
#res.new
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