CD-distance

Chan-Darwiche (CD) distance between a Bayesian network and its update after parameter variation.

Usage

CD(
  bnfit,
  node,
  value_node,
  value_parents,
  new_value,
  covariation = "proportional"
)

Arguments

bnfit: object of class bn.fit.
node: character string. Node of which the conditional probability distribution is being changed.
value_node: character string. Level of node.
value_parents: character string. Levels of node's parents. The levels should be defined according to the order of the parents in bnfit[[node]][["parents"]]. If node has no parents, then it should be set to NULL.
new_value: numeric vector with elements between 0 and 1. Values to which the parameter should be updated. It can take a specific value or more than one. In the case of more than one value, these should be defined through a vector with an increasing order of the elements. new_value can also be set to the character string all: in this case a sequence of possible parameter changes ranging from 0.05 to 0.95 is considered.
covariation: character string. Co-variation scheme to be used for the updated Bayesian network. Can take values uniform, proportional, orderp, all. If equal to all, uniform, proportional and order-preserving co-variation schemes are used. Set by default to proportional.

Value

The function CD returns a dataframe including in the first column the variations performed, and in the following columns the corresponding CD distances for the chosen co-variation schemes.

Details

The Bayesian network on which parameter variation is being conducted should be expressed as a bn.fit object. The name of the node to be varied, its level and its parent's levels should be specified. The parameter variation specified by the function is:

P ( node = value_node | parents = value_parents ) = new_value

The CD distance between two probability distributions $P$ and $P'$ defined over the same sample space $\mathcal{Y}$ is defined as $$CD(P,P')= \log\max_{y\in\mathcal{Y}}\left(\frac{P(y)}{P'(y)}\right) - \log\min_{y\in\mathcal{Y}}\left(\frac{P(y)}{P'(y)}\right)$$

References

Chan, H., & Darwiche, A. (2005). A distance measure for bounding probabilistic belief change. International Journal of Approximate Reasoning, 38(2), 149-174.

Renooij, S. (2014). Co-variation for sensitivity analysis in Bayesian networks: Properties, consequences and alternatives. International Journal of Approximate Reasoning, 55(4), 1022-1042.

Examples