| covariance_var {bnmonitor} | R Documentation |
Standard variation of the covariance matrix
Description
Computation of an updated GBN object after a variation of the covariance matrix.
Usage
covariance_var(gbn, entry, delta)
Arguments
gbn |
object of class |
entry |
a vector of length 2 specifying the entry of the covariance matrix to vary. |
delta |
additive variation coefficient for the entry of the co-variation matrix given in |
Details
Let the original Bayesian network have a Normal distribution \mathcal{N}(\mu,\Sigma) and let entry be equal to (i,j). For a variation of the covariance matrix by an amount \delta, a variation matrix D is constructed as
D_{k,l}=\left\{
\begin{array}{ll}
\delta & \mbox{if } k=i, l=j\\
\delta & \mbox{if } l=i, k=j \\
0 & \mbox{otherwise}
\end{array}
\right.
Then the resulting distribution after the variation is \mathcal{N}(\mu,\Sigma +D), assuming \Sigma+ D is positive semi-definite.
Value
If the resulting covariance is positive semi-definite, covariance_var returns an object of class GBN with an updated covariance matrix. Otherwise it returns an object of class npsd.gbn, which has the same components of GBN but also has a warning entry specifying that the covariance matrix is not positive semi-definite.
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
Examples
covariance_var(synthetic_gbn,c(1,1),3)
covariance_var(synthetic_gbn,c(1,2),-0.4)