## A frequentist semantics for a generalized Jeffrey conditionalization

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