model_pres_cov {bnmonitor} | R Documentation |
Model-Preserving co-variation
Description
Model-preserving co-variation for objects of class CI
.
Usage
model_pres_cov(ci, type, entry, delta)
Arguments
ci |
object of class |
type |
character string. Type of model-preserving co-variation: either |
entry |
a vector of length two specifying the entry of the covariance matrix to vary. |
delta |
multiplicative variation coefficient for the entry of the covariance matrix given in |
Details
Let the original Bayesian network have a Normal distribution and let
entry
be equal to . For a multiplicative variation of the covariance matrix by an amount
, a variation matrix
is constructed as
A co-variation matrix is then constructed and the resulting distribution after the variation is
, assuming
is positive semi-definite and where
denotes the Schur (or element-wise) product. The matrix
is so constructed to ensure that all conditional independence in the original Bayesian networks are retained after the parameter variation.
Value
If the resulting covariance is positive semi-definite, model_pres_cov
returns an object of class CI
with an updated covariance matrix. Otherwise it returns an object of class npsd.ci
, which has the same components of CI
but also has a warning entry specifying that the covariance matrix is not positive semi-definite.
References
C. Görgen & M. Leonelli (2020), Model-preserving sensitivity analysis for families of Gaussian distributions. Journal of Machine Learning Research, 21: 1-32.
See Also
covariance_var
, covariation_matrix
Examples
model_pres_cov(synthetic_ci,"partial",c(1,3),1.1)
model_pres_cov(synthetic_ci,"partial",c(1,3),0.9)
model_pres_cov(synthetic_ci,"total",c(1,2),0.5)
model_pres_cov(synthetic_ci,"row",c(1,3),0.98)
model_pres_cov(synthetic_ci,"column",c(1,3),0.98)