sobol: Monte Carlo Estimation of Sobol' Indices

In sensitivity: Sensitivity Analysis

Description

sobol implements the Monte Carlo estimation of the Sobol' sensitivity indices. This method allows the estimation of the indices of the variance decomposition, sometimes referred to as functional ANOVA decomposition, up to a given order, at a total cost of (N + 1) * n where N is the number of indices to estimate. This function allows also the estimation of the so-called subset indices, i.e. the first-order indices with respect to single multidimensional inputs.

Usage

sobol(model = NULL, X1, X2, order = 1, nboot = 0, conf = 0.95, ...)
## S3 method for class 'sobol'
tell(x, y = NULL, return.var = NULL, ...)
## S3 method for class 'sobol'
print(x, ...)
## S3 method for class 'sobol'
plot(x, ylim = c(0, 1), ...)

Arguments

model	a function, or a model with a predict method, defining the model to analyze.
X1	the first random sample.
X2	the second random sample.
order	either an integer, the maximum order in the ANOVA decomposition (all indices up to this order will be computed), or a list of numeric vectors, the multidimensional compounds of the wanted subset indices.
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.
return.var	a vector of character strings giving further internal variables names to store in the output object x.
ylim	y-coordinate plotting limits.
...	any other arguments for model which are passed unchanged each time it is called.

Value

sobol returns a list of class "sobol", 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.
V	the estimations of Variances of the Conditional Expectations (VCE) with respect to one factor or one group of factors.
D	the estimations of the terms of the ANOVA decomposition (not for subset indices).
S	the estimations of the Sobol' sensitivity indices (not for subset indices).

Users can ask more ouput variables with the argument return.var (for example, bootstrap outputs V.boot, D.boot and S.boot).

References

I. M. Sobol, 1993, Sensitivity analysis for non-linear mathematical model, Math. Modelling Comput. Exp., 1, 407–414.

See Also

sobol2002

Examples

# 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])
n <- 1000
X1 <- data.frame(matrix(runif(8 * n), nrow = n))
X2 <- data.frame(matrix(runif(8 * n), nrow = n))

# sensitivity analysis
x <- sobol(model = sobol.fun, X1 = X1, X2 = X2, order = 2, nboot = 100)
print(x)
#plot(x)

Example output

Call:
sobol(model = sobol.fun, X1 = X1, X2 = X2, order = 2, nboot = 100)

Model runs: 37000 

Sobol indices
          original          bias std. error    min. c.i.  max. c.i.
X1     0.768511063  0.0007268986 0.05012932  0.658158516 0.86439591
X2     0.140229174 -0.0079044206 0.06060970  0.005782988 0.26092960
X3     0.009363961 -0.0094405404 0.06366132 -0.106907999 0.13609935
X4    -0.031649473 -0.0079924660 0.06232238 -0.148386241 0.09611522
X5    -0.013416823 -0.0082005795 0.06295162 -0.125673398 0.12155684
X6    -0.012123780 -0.0083443713 0.06321758 -0.126608148 0.12353326
X7    -0.012292538 -0.0083576475 0.06307308 -0.125944112 0.12266767
X8    -0.013411463 -0.0084403763 0.06304021 -0.126209293 0.12152019
X1*X2  0.063485348  0.0091612164 0.07678676 -0.097505656 0.20465376
X1*X3  0.028045949  0.0080029406 0.06632299 -0.116126141 0.15032207
X1*X4  0.022779490  0.0082781435 0.06341410 -0.108931127 0.13910053
X1*X5  0.012545655  0.0083380562 0.06294747 -0.122207025 0.12662811
X1*X6  0.013827827  0.0082530899 0.06308891 -0.121148462 0.12763385
X1*X7  0.012520805  0.0083131731 0.06306090 -0.122088169 0.12632693
X1*X8  0.013116935  0.0082074013 0.06310566 -0.121588377 0.12730232
X2*X3  0.007401685  0.0080526384 0.06392742 -0.132974200 0.11864049
X2*X4  0.010088694  0.0082868086 0.06301706 -0.127480077 0.12246903
X2*X5  0.013520112  0.0082490902 0.06308507 -0.121451167 0.12751583
X2*X6  0.013813780  0.0083265357 0.06300070 -0.121117693 0.12791120
X2*X7  0.013839285  0.0082877742 0.06300839 -0.120854822 0.12760082
X2*X8  0.013945021  0.0083525654 0.06304440 -0.121303005 0.12751772
X3*X4  0.013349779  0.0084105878 0.06290093 -0.120268758 0.12674229
X3*X5  0.013570454  0.0082863730 0.06305159 -0.121394473 0.12725812
X3*X6  0.013589242  0.0082791046 0.06304565 -0.121377845 0.12727869
X3*X7  0.013623538  0.0082838482 0.06305192 -0.121457490 0.12734158
X3*X8  0.013734527  0.0082831874 0.06305038 -0.121171112 0.12741414
X4*X5  0.013588374  0.0082801069 0.06304150 -0.121361325 0.12724321
X4*X6  0.013558625  0.0082931185 0.06304126 -0.121388935 0.12725220
X4*X7  0.013493024  0.0082863955 0.06304590 -0.121410591 0.12723550
X4*X8  0.013532779  0.0082905033 0.06304030 -0.121385810 0.12719205
X5*X6  0.013542643  0.0082851877 0.06304827 -0.121394454 0.12725147
X5*X7  0.013538355  0.0082840619 0.06304752 -0.121395010 0.12724692
X5*X8  0.013540262  0.0082847543 0.06304791 -0.121389893 0.12725540
X6*X7  0.013529130  0.0082856975 0.06304874 -0.121408076 0.12724878
X6*X8  0.013536114  0.0082841736 0.06304787 -0.121400209 0.12725417
X7*X8  0.013547608  0.0082859475 0.06304702 -0.121387157 0.12725311

sensitivity documentation built on May 2, 2019, 5:56 p.m.