seq_pa_ch_monitor {bnmonitor} | R Documentation |

## Sequential parent-child node monitors

### Description

Sequential node monitor for a vertex of a Bayesian network for a specific configuration of its parents

### Usage

```
seq_pa_ch_monitor(dag, df, node.name, pa.names, pa.val, alpha = "default")
```

### Arguments

`dag` |
an object of class |

`df` |
a base R style dataframe |

`node.name` |
node over which to compute the monitor |

`pa.names` |
vector including the names of the parents of |

`pa.val` |
vector including the levels of |

`alpha` |
single integer. By default, the number of max levels in |

### Details

Consider a Bayesian network over variables `Y_1,\dots,Y_m`

and suppose a dataset `(\boldsymbol{y}_1,\dots,\boldsymbol{y}_n)`

has been observed, where `\boldsymbol{y}_i=(y_{i1},\dots,y_{im})`

and `y_{ij}`

is the i-th observation of the j-th variable.
Consider a configuration `\pi_j`

of the parents and consider the sub-vector `\boldsymbol{y}'=(\boldsymbol{y}_1',\dots,\boldsymbol{y}_{N'}')`

of `(\boldsymbol{y}_1,\dots,\boldsymbol{y}_n)`

including observations where the parents of `Y_j`

take value `\pi_j`

only.
Let `p_i(\cdot|\pi_j)`

be the conditional distribution of `Y_j`

given that its parents take value `\pi_j`

after the first i-1 observations have been processed. Define

`E_i = \sum_{k=1}^Kp_i(d_k|\pi_j)\log(p_i(d_k|\pi_j)),`

`V_i = \sum_{k=1}^K p_i(d_k|\pi_j)\log^2(p_i(d_k|\pi_j))-E_i^2,`

where `(d_1,\dots,d_K)`

are the possible values of `Y_j`

. The sequential parent-child node monitor for the vertex `Y_j`

and parent configuration `\pi_j`

is defined as

`Z_{ij}=\frac{-\sum_{k=1}^i\log(p_k(y_{kj}'|\pi_j))-\sum_{k=1}^i E_k}{\sqrt{\sum_{k=1}^iV_k}}.`

Values of `Z_{ij}`

such that `|Z_{ij}|> 1.96`

can give an indication of a poor model fit for the vertex `Y_j`

after the first i-1 observations have been processed.

### Value

A vector including the scores `Z_{ij}`

.

### References

Cowell, R. G., Dawid, P., Lauritzen, S. L., & Spiegelhalter, D. J. (2006). Probabilistic networks and expert systems: Exact computational methods for Bayesian networks. Springer Science & Business Media.

Cowell, R. G., Verrall, R. J., & Yoon, Y. K. (2007). Modeling operational risk with Bayesian networks. Journal of Risk and Insurance, 74(4), 795-827.

### See Also

`influential_obs`

, `node_monitor`

, `seq_node_monitor`

, `seq_pa_ch_monitor`

### Examples

```
seq_pa_ch_monitor(chds_bn, chds, "Events", "Social", "High", 3)
```

*bnmonitor*version 0.1.4 Index]