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• W1900523596 startingPage "2595" @default.
• W1900523596 abstract "The Borel–Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. The conditional probabilities on probability zero events in the Borel–Kolmogorov Paradox also can be calculated using conditional expectations. The alleged clash arising from the fact that one obtains different values for the conditional probabilities on probability zero events depending on what conditional expectation one uses to calculate them is resolved by showing that the different conditional probabilities obtained using different conditional expectations cannot be interpreted as calculating in different parametrizations of the conditional probabilities of the same event with respect to the same conditioning conditions. We conclude that there is no clash between the correct intuition about what the conditional probabilities with respect to probability zero events are and the technically proper concept of conditionalization via conditional expectations—the Borel–Kolmogorov Paradox is just a pseudo-paradox." @default.
• W1900523596 created "2016-06-24" @default.
• W1900523596 creator A5012683880 @default.
• W1900523596 creator A5037562631 @default.
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• W1900523596 date "2016-03-26" @default.
• W1900523596 modified "2023-09-26" @default.
• W1900523596 title "Conditioning using conditional expectations: the Borel–Kolmogorov Paradox" @default.
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• W1900523596 doi "https://doi.org/10.1007/s11229-016-1070-8" @default.
• W1900523596 hasPublicationYear "2016" @default.
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