Standard variation of the mean vector

Computation of an updated GBN object after a variation of the mean vector.

Usage

mean_var(gbn, entry, delta)

Arguments

gbn

object of class GBN.

entry

an index specifying the entry of the mean vector to vary.

delta

additive variation coefficient for the entry of the mean vector given in entry.

Value

An object of class GBN with an updated mean vector.

Details

Let the original Bayesian network have a Normal distribution \(\mathcal{N}(\mu,\Sigma)\) and let entry be equal to \(i\). Let \(\mu_i\) be the i-th entry of \(\mu\). For a variation of the mean by an amount \(\delta\) the resulting distribution is \(\mathcal{N}(\mu',\Sigma)\), where \(\mu'\) is equal to \(\mu\) except for the i-th entry which is equal to \(\mu+\delta\).

References

Gómez-Villegas, M. A., Maín, P., & Susi, R. (2007). Sensitivity analysis in Gaussian Bayesian networks using a divergence measure. Communications in Statistics—Theory and Methods, 36(3), 523-539.

Gómez-Villegas, M. A., Main, P., & Susi, R. (2013). The effect of block parameter perturbations in Gaussian Bayesian networks: Sensitivity and robustness. Information Sciences, 222, 439-458.

See also

covariance_var

Examples

mean_var(synthetic_gbn,2,3)
#> $order
#> [1] "y1" "y2" "y3" "y4"
#> 
#> $mean
#>      [,1]
#> [1,]    0
#> [2,]    3
#> [3,]    0
#> [4,]    0
#> 
#> $covariance
#>      [,1] [,2] [,3] [,4]
#> [1,]    1    2    2    7
#> [2,]    2    5    5   17
#> [3,]    2    5    6   19
#> [4,]    7   17   19   63
#> 
#> attr(,"class")
#> [1] "GBN"