covariance_var | R Documentation |

Computation of an updated `GBN`

object after a variation of the covariance matrix.

```
covariance_var(gbn, entry, delta)
```

`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 |

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.

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.

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.

`mean_var`

, `model_pres_cov`

```
covariance_var(synthetic_gbn,c(1,1),3)
covariance_var(synthetic_gbn,c(1,2),-0.4)
```

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