Jeffreys.CI returns the Jeffreys divergence between an object of class CI and its update after a model-preserving parameter variation.
Usage
# S3 method for CI
Jeffreys(x, type, entry, delta, ...)Arguments
- x
object of class
CI.- type
character string. Type of model-preserving co-variation: either
"total","partial",row,columnorall. Ifallthe Jeffreys divergence is computed for every type of co-variation matrix.- entry
a vector of length 2 indicating the entry of the covariance matrix to vary.
- delta
numeric vector with positive elements, including the variation parameters that act multiplicatively.
- ...
additional arguments for compatibility.
Value
A dataframe including in the first column the variations performed, and in the following columns the corresponding Jeffreys divergences for the chosen model-preserving co-variations.
Details
Computation of the Jeffreys divergence between a Bayesian network and its updated version after a model-preserving variation.
References
C. Görgen & M. Leonelli (2020), Model-preserving sensitivity analysis for families of Gaussian distributions. Journal of Machine Learning Research, 21: 1-32.
Examples
Jeffreys(synthetic_ci,"total",c(1,1),seq(0.9,1.1,0.01))
#> Variation Jeffreys
#> 1 0.90 4.500000e-01
#> 2 0.91 3.169565e-01
#> 3 0.92 2.215385e-01
#> 4 0.93 1.520690e-01
#> 5 0.94 1.012500e-01
#> 6 0.95 6.428571e-02
#> 7 0.96 3.789474e-02
#> 8 0.97 1.975610e-02
#> 9 0.98 8.181818e-03
#> 10 0.99 1.914894e-03
#> 11 1.00 -1.154632e-14
#> 12 1.01 1.698113e-03
#> 13 1.02 6.428571e-03
#> 14 1.03 1.372881e-02
#> 15 1.04 2.322581e-02
#> 16 1.05 3.461538e-02
#> 17 1.06 4.764706e-02
#> 18 1.07 6.211268e-02
#> 19 1.08 7.783784e-02
#> 20 1.09 9.467532e-02
#> 21 1.10 1.125000e-01
Jeffreys(synthetic_ci,"partial",c(1,4),seq(0.9,1.1,0.01))
#> Variation Jeffreys
#> 1 0.90 NA
#> 2 0.91 5.546515e+00
#> 3 0.92 2.386087e+00
#> 4 0.93 1.401482e+00
#> 5 0.94 9.022547e-01
#> 6 0.95 5.913793e-01
#> 7 0.96 3.758904e-01
#> 8 0.97 2.187536e-01
#> 9 0.98 1.044670e-01
#> 10 0.99 2.921112e-02
#> 11 1.00 -1.154632e-14
#> 12 1.01 4.310592e-02
#> 13 1.02 2.426367e-01
#> 14 1.03 9.874965e-01
#> 15 1.04 1.372000e+01
#> 16 1.05 NA
#> 17 1.06 NA
#> 18 1.07 NA
#> 19 1.08 NA
#> 20 1.09 NA
#> 21 1.10 NA
Jeffreys(synthetic_ci,"column",c(1,2),seq(0.9,1.1,0.01))
#> Variation Jeffreys
#> 1 0.90 NA
#> 2 0.91 NA
#> 3 0.92 NA
#> 4 0.93 NA
#> 5 0.94 NA
#> 6 0.95 3.185714e+00
#> 7 0.96 9.096194e-01
#> 8 0.97 3.480288e-01
#> 9 0.98 1.227907e-01
#> 10 0.99 2.656130e-02
#> 11 1.00 -1.154632e-14
#> 12 1.01 2.354191e-02
#> 13 1.02 9.519481e-02
#> 14 1.03 2.279154e-01
#> 15 1.04 4.603681e-01
#> 16 1.05 9.032787e-01
#> 17 1.06 1.988852e+00
#> 18 1.07 8.363301e+00
#> 19 1.08 NA
#> 20 1.09 NA
#> 21 1.10 NA
Jeffreys(synthetic_ci,"row",c(3,2),seq(0.9,1.1,0.01))
#> Variation Jeffreys
#> 1 0.90 NA
#> 2 0.91 NA
#> 3 0.92 NA
#> 4 0.93 NA
#> 5 0.94 NA
#> 6 0.95 NA
#> 7 0.96 NA
#> 8 0.97 2.844994e+00
#> 9 0.98 4.140902e-01
#> 10 0.99 6.394370e-02
#> 11 1.00 -1.154632e-14
#> 12 1.01 3.898137e-02
#> 13 1.02 1.359300e-01
#> 14 1.03 2.800207e-01
#> 15 1.04 4.769514e-01
#> 16 1.05 7.504484e-01
#> 17 1.06 1.161735e+00
#> 18 1.07 1.889495e+00
#> 19 1.08 3.716283e+00
#> 20 1.09 2.343924e+01
#> 21 1.10 NA
Jeffreys(synthetic_ci,"all",c(3,2),seq(0.9,1.1,0.01))
#> Variation Total Partial Row_based Column_based
#> 1 0.90 2.222222e-02 NA NA NA
#> 2 0.91 1.780220e-02 NA NA NA
#> 3 0.92 1.391304e-02 NA NA NA
#> 4 0.93 1.053763e-02 NA NA NA
#> 5 0.94 7.659574e-03 NA NA NA
#> 6 0.95 5.263158e-03 NA NA NA
#> 7 0.96 3.333333e-03 NA NA NA
#> 8 0.97 1.855670e-03 NA 2.844994e+00 NA
#> 9 0.98 8.163265e-04 1.798459e+00 4.140902e-01 8.333333e-01
#> 10 0.99 2.020202e-04 1.433278e-01 6.394370e-02 9.877622e-02
#> 11 1.00 -1.154632e-14 -1.154632e-14 -1.154632e-14 -1.154632e-14
#> 12 1.01 1.980198e-04 6.294876e-02 3.898137e-02 5.092593e-02
#> 13 1.02 7.843137e-04 2.002346e-01 1.359300e-01 1.691176e-01
#> 14 1.03 1.747573e-03 3.786784e-01 2.800207e-01 3.331882e-01
#> 15 1.04 3.076923e-03 5.882775e-01 4.769514e-01 5.416667e-01
#> 16 1.05 4.761905e-03 8.280151e-01 7.504484e-01 8.068182e-01
#> 17 1.06 6.792453e-03 1.102738e+00 1.161735e+00 1.161290e+00
#> 18 1.07 9.158879e-03 1.423943e+00 1.889495e+00 1.686594e+00
#> 19 1.08 1.185185e-02 1.814278e+00 3.716283e+00 2.631579e+00
#> 20 1.09 1.486239e-02 2.320121e+00 2.343924e+01 5.245482e+00
#> 21 1.10 1.818182e-02 3.050000e+00 NA NA