estimateGraph: FANOVA graph estimation.

In fanovaGraph: Building Kriging Models from FANOVA Graphs

Description

Estimates the structure of the FANOVA graph by estimating the total interaction indices for the graph edges (a particular case of superset importance introduced by Liu and Owen, 2006), the main effect indices for the graph vertices and the overall variance for normalizing the indices and finding the clique structure of the estimated graph.

Usage

estimateGraph(f.mat, d, q = NULL, q.arg = NULL, n.tot = NULL, method = "LiuOwen", 
n.lo = NULL, n.mc = NULL, n.fast = 500, L = NULL, M = 6, n.pf = NULL, n.main = 1000, 
confint = TRUE, print.loop.index = FALSE, ...)

Arguments

f.mat	vectorized function for which the FANOVA graph shall be estimated
d	integer, number of input factors (vertices)
q	a vector of character strings of quantile functions corresponding to the factors distributions, it can be a single character string meaning same distribution for all, if not specified "qunif" is taken
q.arg	a list of lists of quantile functions parameters of the distributions in q, it can be a single list meaning same parameters for all, if not specified the default values of the respective distributions are taken
n.tot	optional integer, total number of function evaluations, instead of n.tot method related parameters (n.lo, n.mc, L or n.sobol) can be provided
method	character string specifying the estimation method of the total interaction indices, to be chosen between "LiuOwen", "FixFast", "RBD" and "PickFreeze", defaults to "LiuOwen", see references for further details
n.lo	optional integer, only if method="LiuOwen", number of Monte Carlo simulations in method of Liu and Owen
n.mc	optional integer, only if method="FixFast", number of Monte Carlo simulations for the expectation in fixing method using FAST
n.fast	optional integer, only if method="FixFast", number of design points for FAST algorithm, defaults to 500
L	optional integer, only if method="RBD", parameter L in RBD-FAST method
M	optional integer, only if method="RBD", parameter M in RBD-FAST method
n.pf	optional integer, only if method="PickFreeze", number of Monte Carlo simulations in pick-and-freeze method
n.main	integer, number of Monte Carlo Simulations for computing main effect indices
confint	optional Boolean, if TRUE, standard error and 95% confidence intervals of the indices are computed additionally for method="LiuOwen", defaults to TRUE
print.loop.index	optional Boolean, if TRUE, loop indices are printed
...	additional arguments to be passed to the function f.mat

Value

an object of class graphlist containing the graph structure which includes

d	number of input factors
tii	matrix containing the unscaled total interaction indices and if confint = TRUE their standard error and lower and upper confidence limits
i1	matrix containing the unscaled main effect indices
V	overall variance
tii.scaled	matrix containing the scaled total interaction indices
cliques	list of cliques

Author(s)

J. Fruth, T. Muehlenstaedt

References

Fruth, J.; Roustant, O.; Kuhnt, S. (2013+) Total interaction index: A variance-based sensitivity index for second-order interaction screening.

Janon, A.; Klein, T.; Lagnoux, A.; Nodet, M.; Prieur, C. (2013) Asymptotic normality and efficiency of two Sobol index estimators.

Liu, R.; Owen, A.B. (2006) Estimating mean dimensionality of analysis of variance decompositions, Journal of the American Statistical Association, 101 474, 712-721.

Mara, T.A (2009) Extension of the RBD-FAST method to the computation of global sensitivity indices, Reliability Engineering & System Safety, 94 no. 8, 1274-1281.

Muehlenstaedt, T.; Roustant, O.; Carraro, L.; Kuhnt, S. (2011) Data-driven Kriging models based on FANOVA-decomposition, Statistics and Computing.

Sobol', I. M. (1993) Sensitivity estimates for nonlinear mathematical models, Mathematical Modeling and Computational Experiment, 1, 407-414.

Examples

# Ishigami function, true analytical values: D12 = D23 = 0, D13 =~ 3.374
q.arg = list(list(min=-pi, max=pi), list(min=-pi, max=pi), list(min=-pi, max=pi)) 
estimateGraph(f.mat=ishigami.fun, d=3, q.arg=q.arg, n.tot=10000, method="LiuOwen")
estimateGraph(f.mat=ishigami.fun, d=3, q.arg=q.arg, n.tot=10000, method="FixFast")
estimateGraph(f.mat=ishigami.fun, d=3, q.arg=q.arg, n.tot=10000, method="RBD")
estimateGraph(f.mat=ishigami.fun, d=3, q.arg=q.arg, n.tot=10000, method="PickFreeze")

Example output

Loading required package: sensitivity
Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

Loading required package: DiceKriging
Warning message:
no DISPLAY variable so Tk is not available 
Overall variance
[1] 13.55881

Cliques
2 
13 

Scaled total interaction indices
       totalInt
X1*X2 0.0000000
X1*X3 0.2722276
X2*X3 0.0000000
Overall variance
[1] 14.52122

Cliques
123 

Scaled total interaction indices
             [,1]
X1*X2 0.002099524
X1*X3 0.227098323
X2*X3 0.003716544
Overall variance
[1] 13.88653

Cliques
13 
23 

Scaled total interaction indices
              [,1]
X1*X2 -0.001761127
X1*X3  0.310391559
X2*X3  0.019999125
Overall variance
[1] 13.73376

Cliques
13 
12 

Scaled total interaction indices
              [,1]
X1*X2  0.003757655
X1*X3  0.253974431
X2*X3 -0.023405432

fanovaGraph documentation built on Oct. 23, 2020, 5:46 p.m.