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. Define \(\boldsymbol{y}_{-i}=(\boldsymbol{y}_1,\dots,\boldsymbol{y}_{i-1},\boldsymbol{y}_{i+1},\dots,\boldsymbol{y}_n)\).
The influence of an observation to the global monitor is defined as
$$|\log(p(\boldsymbol{y}_1,\dots,\boldsymbol{y}_n)) - \log(p(\boldsymbol{y}_{-i}))|.$$
High values of this index denote observations that highly contribute to the likelihood of the model.