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Figure 1E H shows positional variance diagrams obtained from cross-validation of the maximum likelihood ordering.
> Figure 1A D shows positional variance diagrams for each population subgroup.
The positional variance diagrams for the cross validation results show the proportion of bootstrap samples in which event appears at position of the maximum likelihood sequence.
The uncertainty in the event sequence, as shown by the positional variance diagrams and cross-validation results, potentially provides useful information about the variation of biomarker ordering across the population.
However, it is important to remember that the single sequence does not represent all subjects and the positional variance diagrams are only a crude indicator of heterogeneity of the event sequence.
The positional variance diagrams generated directly from the EBM (Fig. 1A D) underestimate the uncertainty in the event ordering, as they do not account for uncertainty in the biomarker distribution models.
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Each positional variance diagram shows the maximum likelihood event sequence and its uncertainty.
It is thus important to consider not only the most likely sequence, but also the positional variance diagram and cross-validation output, which explicitly highlight areas of uncertainty, aiding interpretation particularly where the data depart from the assumptions, for example in heterogeneous groups.
The positional variance diagram (Fonteijn et al., 2012) (Fig. 1A D) visualizes both the maximum likelihood sequence and its uncertainty by plotting the likelihood that each event appears in each position in the sequence, i.e. the entry of each position is where is the set of all sequences with event at position.
The resulting variance vs. depth diagram indicates the optimal depth as a clear variance minimum (Figure 5).
A variance versus depth diagram from the moment tensor inversion yields the optimum solution as a clear minimum (red focal mechanism) at 18 km depth.
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