sobol2002: Monte Carlo Estimation of Sobol' Indices (scheme by Saltelli...

In sensitivity: Sensitivity Analysis

Description

sobol2002 implements the Monte Carlo estimation of the Sobol' indices for both first-order and total indices at the same time (alltogether 2p indices), at a total cost of (p + 2) * n model evaluations.

Usage

sobol2002(model = NULL, X1, X2, nboot = 0, conf = 0.95, ...)
## S3 method for class 'sobol2002'
tell(x, y = NULL, return.var = NULL, ...)
## S3 method for class 'sobol2002'
print(x, ...)
## S3 method for class 'sobol2002'
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.
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

sobol2002 returns a list of class "sobol2002", 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	the response used
V	the estimations of Variances of the Conditional Expectations (VCE) with respect to each factor and also with respect to the complementary set of each factor ("all but Xi").
S	the estimations of the Sobol' first-order indices.
T	the estimations of the Sobol' total sensitivity indices.

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

References

A. Saltelli, 2002, Making best use of model evaluations to compute sensitivity indices, Computer Physics Communication, 145, 580–297.

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 <- sobol2002(model = sobol.fun, X1, X2, nboot = 100)
print(x)
plot(x)

Example output

Call:
sobol2002(model = sobol.fun, X1 = X1, X2 = X2, nboot = 100)

Model runs: 10000 

First order indices:
      original          bias   std. error     min. c.i.   max. c.i.
X1 0.772663777 -3.505939e-04 0.0735226793  0.5941208077 0.931199301
X2 0.181521631  4.835765e-03 0.0428905091  0.0885254055 0.259131025
X3 0.032407185 -1.124696e-03 0.0150697862  0.0017941259 0.058114904
X4 0.007928388 -4.749885e-04 0.0085572470 -0.0102727687 0.026694593
X5 0.000455648  3.136872e-05 0.0007955689 -0.0014202715 0.001919533
X6 0.002572585 -3.051926e-05 0.0006641615  0.0012351322 0.003883425
X7 0.002644076  1.061585e-04 0.0009785932  0.0007101465 0.004512303
X8 0.001962201  5.097122e-05 0.0008890980  0.0001361504 0.003671878

Total indices:
        original          bias  std. error    min. c.i.    max. c.i.
X1  0.6890511145  5.425975e-06 0.058730781  0.581259379  0.821196296
X2  0.2217119642 -5.534338e-03 0.052271693  0.136215148  0.347241490
X3  0.0344540099 -1.138559e-03 0.024066477 -0.013418609  0.089228372
X4  0.0164565906  1.218419e-03 0.011754435 -0.005732779  0.042893826
X5 -0.0002920481 -1.112492e-05 0.001184130 -0.002517972  0.002187899
X6 -0.0041463566  4.704660e-05 0.001044492 -0.006396229 -0.002198296
X7 -0.0041774574 -9.950025e-05 0.001204040 -0.006646766 -0.001913350
X8 -0.0013667056 -1.527023e-04 0.001303396 -0.003761693  0.001161511

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