seq_pa_ch_monitor {bnmonitor} | R Documentation |
Sequential node monitor for a vertex of a Bayesian network for a specific configuration of its parents
seq_pa_ch_monitor(dag, df, node.name, pa.names, pa.val, alpha = "default")
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 |
Consider a Bayesian network over variables Y_1,…,Y_m and suppose a dataset (\boldsymbol{y}_1,…,\boldsymbol{y}_n) has been observed, where \boldsymbol{y}_i=(y_{i1},…,y_{im}) and y_{ij} is the i-th observation of the j-th variable. Consider a configuration π_j of the parents and consider the sub-vector \boldsymbol{y}'=(\boldsymbol{y}_1',…,\boldsymbol{y}_{N'}') of (\boldsymbol{y}_1,…,\boldsymbol{y}_n) including observations where the parents of Y_j take value π_j only. Let p_i(\cdot|π_j) be the conditional distribution of Y_j given that its parents take value π_j after the first i-1 observations have been processed. Define
E_i = ∑_{k=1}^Kp_i(d_k|π_j)\log(p_i(d_k|π_j)),
V_i = ∑_{k=1}^K p_i(d_k|π_j)\log^2(p_i(d_k|π_j))-E_i^2,
where (d_1,…,d_K) are the possible values of Y_j. The sequential parent-child node monitor for the vertex Y_j and parent configuration π_j is defined as
Z_{ij}=\frac{-∑_{k=1}^i\log(p_k(y_{kj}'|π_j))-∑_{k=1}^i E_k}{√{∑_{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.
A vector including the scores Z_{ij}.
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.
influential_obs
, node_monitor
, seq_node_monitor
, seq_pa_ch_monitor
seq_pa_ch_monitor(chds_bn, chds, "Events", "Social", "High", 3)