A frequentist semantics for a generalized Jeffrey conditionalization

Dirk Draheim

Dept. of Informatics
Tallinn University of Technology

Thursday, 5 May 2016, 14:00
Cybernetica Bldg (Akadeemia tee 21), room B101

Slides from the talk [pdf]

Abstract: We introduce a notion of conditional probability that deals with partial knowledge. This notion of probability is conditional on a list of event-probability specifications which we denote as P(A|B.1=b.1,...,B.n=b.n). We call it frequentist partial knowledge conditionalization, or F.P. conditionalization for short. 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. With our frequentist semantics we are able to generalize Jeffrey conditionalization further. Jeffrey conditionalization treats the special case of complete decompositions, 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. Furthermore, we will be able to explain the effect of mutually independency of conditions. Furthermore, we will be able to characterize the decomposition of conditionalization and show how to compute arbitrary precise approximations of a conditionalization. With our semantics, we do not need to stay vague about the interpretation of new vs. old probabilities and the transition amongst them. We do not need to stress psychological metaphors like degrees of belief and do not need to search for any kind of possible world semantics. This way, our semantics may also contribute to mitigate the gap between Bayesian epistemology and the classic, frequentist world-view of probability.

Tarmo Uustalu
Last update 5 May 2016