| 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,])