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Bayes rules all: On the equivalence of various forms of learning in a probabilistic setting

Gyenis, Balazs (2014) Bayes rules all: On the equivalence of various forms of learning in a probabilistic setting. [Preprint]

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Jeffrey conditioning is said to provide a more general method of assimilating uncertain evidence than Bayesian conditioning. We show that Jeffrey learning is merely a particular type of Bayesian learning if we accept either of the following two observations:
– Learning comprises both probability kinematics and proposition kinematics.
– What can be updated is not the same as what can do the updating; the set of the latter is richer than the set of the former.
We address the problem of commutativity and isolate commutativity from invariance upon conditioning on conjunctions. We also present a disjunctive model of Bayesian learning which suggests that Jeffrey conditioning is better understood as providing a method for incorporating unspecified but certain evidence rather than providing a method for incorporating specific but uncertain evidence. The results also generalize over many other subjective probability update rules, such as those proposed by Field (1978) and Gallow (2014).

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Item Type: Preprint
Keywords: Bayesian learning, Jeffrey conditioning, Gallow conditioning, commutativity, formal epistemology
Subjects: General Issues > Confirmation/Induction
General Issues > Formal Learning Theory
Specific Sciences > Probability/Statistics
Depositing User: Dr. Balazs Gyenis
Date Deposited: 28 Dec 2014 16:42
Last Modified: 28 Dec 2014 16:42
Item ID: 11230

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