Detecting correlation between extreme probability events

Abstract

Since the classical definitions of correlation give rise to counterintuitive findings for extreme probability events, we build upon the concept of coherent conditional probability to introduce enhanced notions of correlation. Our new notions allow handling extreme events in a principled way by accommodating the different levels of strength of the zero probabilities involved. Where the detection of correlations by means of these levels is computationally challenging, we provide a full characterisation of the correlations between extreme probability events without reference to the complex structure of probability.