`sobol2007`

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. These are called the Mauntz estimators.

1 2 3 4 5 6 7 |

`model` |
a function, or a model with a |

`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 |

`y` |
a vector of model responses. |

`return.var` |
a vector of character strings giving further
internal variables names to store in the output object |

`ylim` |
y-coordinate plotting limits. |

`...` |
any other arguments for |

This estimator is good for small first-order and total indices.

BE CAREFUL! This estimator suffers from a conditioning problem when estimating
the variances behind the indices computations. This can seriously affect the
Sobol' indices estimates in case of largely non-centered output. To avoid this
effect, you have to center the model output before applying `"sobol2007"`

.
Functions `"sobolEff"`

, `"soboljansen"`

and `"sobolmartinez"`

do not suffer from this problem.

`sobol2007`

returns a list of class `"sobol2007"`

, containing all
the input arguments detailed before, plus the following components:

`call` |
the matched call. |

`X` |
a |

`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 |

`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`

).

Bertrand Iooss

I.M. Sobol, S. Tarantola, D. Gatelli, S.S. Kucherenko and W. Mauntz, 2007, *Estimating
the approximation errors when fixing unessential factors in global sensitivity analysis*,
Reliability Engineering and System Safety, 92, 957–960.

A. Saltelli, P. Annoni, I. Azzini, F. Campolongo, M. Ratto and S. Tarantola, 2010,
*Variance based sensitivity analysis of model output. Design and estimator for the
total sensitivity index*, Computer Physics Communications 181, 259–270.

`sobol, sobol2002, sobolSalt, soboljansen, sobolmartinez, sobolEff, sobolmara,sobolMultOut`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# 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]
library(boot)
n <- 1000
X1 <- data.frame(matrix(runif(8 * n), nrow = n))
X2 <- data.frame(matrix(runif(8 * n), nrow = n))
# sensitivity analysis
x <- sobol2007(model = sobol.fun, X1, X2, nboot = 100)
print(x)
plot(x)
``` |

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