cell column on the $X$ axis and each longitudinal cell strand on the $Y$ axis – this is an adaptation of the regression style models typical in Random Forests in which a continuous scale is broken into discrete ranges and each of the ranges is considered its own class. The benefits of the probabilistic approach over typical regression models is that it is easier to implement additional levels of post-processing in any predictions. The probability of the re-entrant circuit lying in each class can then be processed to infer the predicted position of the re-entrant circuit in a given direction. The probabilistic models can be made from classification (qualitative) models where instead of the majority rule, the response is given by $$P_i = \frac{k_i}{k}, \text{ with} ~ k = \sum_{i=1}^K k_i,$$

where $P_i$ is the probability for the particular response $i$, $k_i$ is the number of data samples that have response $i$ and $k$ is the total number of responses. These probabilities do not consider that electrogram measurements may have been taken previously which gave information as to the direction of the re-entrant circuit from particular regions in the tissue. The post-processing procedures described in appendix \[sec:ap4\] account for this.

