CD {bnmonitor} R Documentation

## CD-distance

### Description

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.

### 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}}≤ft(\frac{P(y)}{P'(y)}\right) - \log\min_{y\in\mathcal{Y}}≤ft(\frac{P(y)}{P'(y)}\right)

### 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.

### 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.

KL.bn.fit
CD(synthetic_bn, "y2", "1", "2", "all", "all")