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 GBN. 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 entry.

### Details

Let the original Bayesian network have a Normal distribution \mathcal{N}(μ,Σ) and let entry be equal to (i,j). For a variation of the covariance matrix by an amount δ, a variation matrix D is constructed as

D_{k,l}=≤ft\{ \begin{array}{ll} δ & \mbox{if } k=i, l=j\\ δ & \mbox{if } l=i, k=j \\ 0 & \mbox{otherwise} \end{array} \right.

Then the resulting distribution after the variation is \mathcal{N}(μ,Σ +D), assuming Σ+ 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.

mean_var, model_pres_cov
covariance_var(synthetic_gbn,c(1,1),3)