This book provides a frequentist semantics for conditionalization on
partially known events, which is given as a straightforward
generalization of classical conditional probability via so-called
probability testbeds. It analyzes the resulting partial
conditionalization, called frequentist partial (F.P.)
conditionalization, from different angles, i.e., with respect to
partitions, segmentation, independence, and chaining. It turns out
that F.P. conditionalization meets and generalizes Jeffrey
conditionalization, i.e., from partitions to arbitrary collections of
events, opening it for reassessment and a range of potential
applications. A counterpart of Jeffrey’s rule for the case of
independence holds in our frequentist semantics. This result is
compared to Jeffrey’s commutative chaining of independent updates.
The postulate of Jeffrey's probability kinematics, which is rooted in
the subjectivism of Frank P. Ramsey, is found to be a consequence in
our frequentist semantics. This way the book creates a link between
the Kolmogorov system of probability and one of the important Bayesian
frameworks. Furthermore, it shows a preservation result for
conditional probabilities under the full update range and compares
F.P. semantics with an operational semantics of classical conditional
probability in terms of so-called conditional events. Lastly, it looks
at the subjectivist notion of desirabilities and proposes a more
fine-grained analysis of desirabilities a posteriori. This book
appeals to researchers who are involved in any kind of knowledge
processing systems. F.P. conditionalization is a straightforward,
fundamental concept that fits human intuition, and is systematically
linked to one of the important Bayesian frameworks. As such, the book
is interesting for anybody investigating the semantics of reasoning
systems.
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Produktdetaljer
ISBN
9783319698687
Publisert
2018
Utgiver
Vendor
Springer
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter