Detecting correlation between extreme probability events

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

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

Detecting correlation between extreme probability events

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