Detecting Correlation Between Extreme Probability Events

As classical definitions of correlation give rise to counterintuitive statements when extreme probability events are involved, we introduce enhanced notions of positive and negative correlation in the general framework of coherent conditional probability. These notions allow to handle extreme probability events in a principled way by accommodating the different levels of strength of the zero probabilities involved (namely, zero layers). Since the detection of correlations by means of zero layers is computationally challenging, we provide a full characterization relying on only conditional probability values.