Jeffreys Divergence for GBN — Jeffreys.GBN • bnmonitor

Jeffreys.GBN returns the Jeffreys divergence between an object of class GBN and its update after a standard parameter variation.

Usage

# S3 method for GBN
Jeffreys(x, where, entry, delta, ...)

Arguments

x: object of class GBN.
where: character string: either mean or covariance for variations of the mean vector and covariance matrix respectively.
entry: if where == "mean", entry is the index of the entry of the mean vector to vary. If where == "covariance", entry is a vector of length 2 indicating the entry of the covariance matrix to vary.
delta: numeric vector, including the variation parameters that act additively.
...: additional arguments for compatibility.

Value

A dataframe including in the first column the variations performed and in the second column the corresponding Jeffreys divergences.

Details

Computation of the Jeffreys divergence between a Bayesian network and the additively perturbed Bayesian network, where the perturbation is either to the mean vector or to the covariance matrix.

References

Goergen, C., & Leonelli, M. (2018). Model-preserving sensitivity analysis for families of Gaussian distributions. arXiv preprint arXiv:1809.10794.

Examples

Jeffreys(synthetic_gbn,"mean",2,seq(-1,1,0.1))
#>    Variation Jeffreys
#> 1       -1.0     3.00
#> 2       -0.9     2.43
#> 3       -0.8     1.92
#> 4       -0.7     1.47
#> 5       -0.6     1.08
#> 6       -0.5     0.75
#> 7       -0.4     0.48
#> 8       -0.3     0.27
#> 9       -0.2     0.12
#> 10      -0.1     0.03
#> 11       0.0     0.00
#> 12       0.1     0.03
#> 13       0.2     0.12
#> 14       0.3     0.27
#> 15       0.4     0.48
#> 16       0.5     0.75
#> 17       0.6     1.08
#> 18       0.7     1.47
#> 19       0.8     1.92
#> 20       0.9     2.43
#> 21       1.0     3.00
Jeffreys(synthetic_gbn,"covariance",c(3,3),seq(-1,1,0.1))
#>    Variation      Jeffreys
#> 1       -1.0            NA
#> 2       -0.9            NA
#> 3       -0.8            NA
#> 4       -0.7            NA
#> 5       -0.6            NA
#> 6       -0.5            NA
#> 7       -0.4            NA
#> 8       -0.3            NA
#> 9       -0.2            NA
#> 10      -0.1  2.500000e-01
#> 11       0.0 -5.773160e-15
#> 12       0.1  8.333333e-02
#> 13       0.2  2.500000e-01
#> 14       0.3  4.500000e-01
#> 15       0.4  6.666667e-01
#> 16       0.5  8.928571e-01
#> 17       0.6  1.125000e+00
#> 18       0.7  1.361111e+00
#> 19       0.8  1.600000e+00
#> 20       0.9  1.840909e+00
#> 21       1.0  2.083333e+00

Jeffreys Divergence for `GBN`