Matthiew Aldridge (University of Leeds) – Six versions of size-bias

The (1) size-bias of a non-negative random variable comes about by weighting each outcome x proportionally to the value x. We can experience size-bias by accident though poor statistical design, or on purpose when we "view the data from the data's point of view". I want to argue that, when dealing with discrete count random variables, a (2) "reduced size-bias", which is 1 less than the usual size-bias, has nicer properties. We'll also look at versions of the size-bias and reduced size-bias for multivariate random vectors (3 & 4), and for random measures and point processes (5 & 6), with the latter behaving similarly to Palm measures and Palm processes. This is a research-in-progress talk.