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  1. Jeffrey Meets Kolmogorov: A General Theory of Conditioning.Alexander Meehan & Snow Zhang - 2020 - Journal of Philosophical Logic 49 (5):941-979.
    Jeffrey conditionalization is a rule for updating degrees of belief in light of uncertain evidence. It is usually assumed that the partitions involved in Jeffrey conditionalization are finite and only contain positive-credence elements. But there are interesting examples, involving continuous quantities, in which this is not the case. Q1 Can Jeffrey conditionalization be generalized to accommodate continuous cases? Meanwhile, several authors, such as Kenny Easwaran and Michael Rescorla, have been interested in Kolmogorov’s theory of regular conditional distributions as a possible (...)
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  • Interpretive Implications of the Sample Space.Dan D. November - unknown
    In this paper I claim that Kolmogorov's probability theory has other basic notions in addition to 'probability' and 'event'. These notions are described by the sample space component of his probability space structure. This claim has several interesting consequences, two of which I discuss in this paper. The major consequence is that the main interpretations of probability theory are in fact not interpretations of Kolmogorov's theory, simply because an interpretation of a mathematical theory in a strict sense must explicate all (...)
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  • A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization.Michael Rescorla - unknown
    This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.
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  • Conditional Degree of Belief and Bayesian Inference.Jan Sprenger - 2020 - Philosophy of Science 87 (2):319-335.
    Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...)
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  • Full & Partial Belief.Konstantin Genin - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 437-498.
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  • Conditional Probabilities.Kenny Easwaran - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198.
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  • General Properties of Bayesian Learning as Statistical Inference Determined by Conditional Expectations.Zalán Gyenis & Miklós Rédei - 2017 - Review of Symbolic Logic 10 (4):719-755.
    We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...)
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  • A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization.Michael Rescorla - 2018 - Review of Symbolic Logic 11 (4):705-735.
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