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")A vector including the scores \(Z_{ij}\).
an object of class bn from the bnlearn package
a base R style dataframe
node over which to compute the monitor
vector including the names of the parents of node.name
vector including the levels of pa.names considered
single integer. By default, the number of max levels in df
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.
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)
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