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Generalized Jeffrey Conditionalization - A Frequentist Semantics of Partial Conditionalization (Paperback, 1st ed. 2017)
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Generalized Jeffrey Conditionalization - A Frequentist Semantics of Partial Conditionalization (Paperback, 1st ed. 2017)
Series: SpringerBriefs in Computer Science
Expected to ship within 10 - 15 working days
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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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