final_node_monitor {bnmonitor} | R Documentation |

## Final node monitors

### Description

Marginal and conditional node monitors over the last observation of the data for all vertices of a Bayesian network using the full dataset

### Usage

```
final_node_monitor(dag, df)
```

### Arguments

`dag` |
an object of class |

`df` |
a base R style dataframe |

### 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.
Let `p_n`

denote the marginal density of `Y_j`

after the first `n-1`

observations have been processed. Define

`E_n = \sum_{k=1}^Kp_n(d_k)\log(p_n(d_k)),`

`V_n = \sum_{k=1}^K p_n(d_k)\log^2(p_n(d_k))-E_n^2,`

where `(d_1,\dots,d_K)`

are the possible values of `Y_j`

. The marginal node monitor for the vertex `Y_j`

is defined as

`Z_j=\frac{-\log(p_n(y_{ij}))- E_n}{\sqrt{V_n}}.`

Higher values of `Z_j`

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

.

The conditional node monitor for the vertex `Y_j`

is defined as

`Z_j=\frac{-\log(p_n(y_{nj}|y_{n1},\dots,y_{n(j-1)},y_{n(j+1)},\dots,y_{nm}))- E_n}{\sqrt{V_n}},`

where `E_n`

and `V_n`

are computed with respect to `p_n(y_{nj}|y_{n1},\dots,y_{n(j-1)},y_{n(j+1)},\dots,y_{nm})`

. Again, higher values of `Z_j`

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

.

### Value

A dataframe including the names of the vertices, the marginal node monitors and the conditional node monitors. It also return two plots where vertices with a darker color have a higher marginal z-score or conditional z-score, respectively, in absolute value.

### 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

```
final_node_monitor(chds_bn, chds[1:100,])
```

*bnmonitor*version 0.1.4 Index]