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 |

`node` |
character string. Node of which the conditional probability distribution is being changed. |

`value_node` |
character string. Level of |

`value_parents` |
character string. Levels of |

`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. |

`covariation` |
character string. Co-variation scheme to be used for the updated Bayesian network. Can take values |

### 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)`

### 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.

### See Also

### Examples

```
CD(synthetic_bn, "y2", "1", "2", "all", "all")
CD(synthetic_bn, "y1", "2", NULL, 0.3, "all")
```

*bnmonitor*version 0.1.4 Index]