11.dets, 14:00 ICT-315 seminar "Generalized Jeffrey Conditionalization - a Frequentist Semantics of Partial Conditionalization"
Tarkvarateaduse instituudi seminaril räägib prof. Dirk Draheim teemal
"Generalized Jeffrey Conditionalization - a Frequentist Semantics of Partial Conditionalization"
We introduce a frequentist semantics for conditionalization on partially known events. This notion of probability is conditional on a list of event-probability specifications, and we denote it as P(A|B1=b1,...,Bn=bn). We call it frequentist partial (F.P.) conditionalization. As in Jeffrey conditionalization, a specification pair B=b stands for the assumption that the probability of B has somehow changed from a previously given, a priori probability into a new, a posteriori probability. We give a formal, frequentist semantics to this kind of conditionalization. We think of conditionalization as taking place in chains of repeated experiments, so-called probability testbeds, of sufficient lengths. We prove that F.P. conditionalization meets Jeffrey conditionalization. Jeffrey conditionalization treats the special case of partitions, i.e., the case in which all of the events are mutually disjoint and sum up to a probability of 100%. With our semantics, these requirements can be dropped so that we can deal with arbitrary lists of overlapping events. This way, F.P. conditionalization generalizes Jeffrey conditionalization, opening it for reassessment and a range of potential applications. The postulate of Jeffrey's probability kinematics, which is rooted in the subjectivism of Frank P. Ramsey, turns out to be a consequence in our frequentist semantics. This way, F.P. conditionalization bridges between the Kolmogorov system of probability and one of the important Bayesian frameworks.