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    The prior distribution over hypotheses faces an interpret... — Carmelics
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    The prior distribution over hypotheses faces an interpretation problem

    SkepticismTruth & Knowledge
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    2 reasons for
    1 reason against

    Reasons For

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    Reason for 1 of 2
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    • 1.Priors over hypotheses cannot be grounded in frequency data, as hypotheses are singular non-repeatable entities (de Finetti's exchangeability theorem has limits).
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    • 2.Subjective probability interpretations (Ramsey, Savage) require priors to be revealed through betting behavior, but no finite betting sequence uniquely determines a prior over hypothesis spaces.
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    • 3.Without a behavioral or frequentist grounding, the prior remains an uninterpreted formal object, making Bayesian inference epistemically circular.
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    Reason for 2 of 2
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    • 1.Jeffreys' non-informative priors produce paradoxes under reparametrization, showing no canonical 'ignorance' prior exists (Bertrand's paradox generalized to measure theory).
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    • 2.If neither subjective nor objective interpretations yield a determinate prior, the prior distribution lacks a principled semantic foundation across any interpretation.
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    Reasons Against

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    Reason against
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    • 1.For a prior to be interpreted as belief (understood as willingness to act), it must make itself apparent in behavior
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    • 2.It is unclear how the prior distribution manifests in behavior
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    Related

    For a prior to be interpreted as belief (understood as willingness to act), it m...If neither subjective nor objective interpretations yield a determinate prior, t...It is unclear how the prior distribution manifests in behaviorJeffreys' non-informative priors produce paradoxes under reparametrization, show...
    +3 moreShow less
    Priors over hypotheses cannot be grounded in frequency data, as hypotheses are s...Subjective probability interpretations (Ramsey, Savage) require priors to be rev...Without a behavioral or frequentist grounding, the prior remains an uninterprete...

    Similar

    The prior distribution over statistical hypotheses can be interpreted ...87%Fiducial probability derives a probability assignment over hypotheses ...79%Representation theorems equate a prior distribution over statistical h...79%Choosing prior distributions objectively falls outside the scope of Ba...76%

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    Notice that all this makes one aspect of the interpretation problem of Section 4.2.1 reappear: how will the prior distribution over hypotheses make itself apparent in behavior, so that it can rightfully be interpreted in terms of belief, here understood as a willingness to act? One response to this question is to turn to different motivations for representing degrees of beliefs by means of probability assignments. Following work by De Finetti, several authors have proposed vindications of pro
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