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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Perspectives
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    Home/Original/inverse
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    Inverse View

    It is not the case that The fiducial argument allows construction of a probability distribution over parameter values based on the observed sample.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The fiducial argument illicitly treats θ as a random variable after conditioning on data, violating the frequentist prohibition on parameter distributions.
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    • 2.Fixing the observed sample s does not transform a sampling distribution over statistics into a legitimate probability distribution over fixed parameters without a prior.
      ?

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    • 3.Savage, Lindley, and others demonstrated that fiducial distributions are not coherent probabilities—they fail additivity when derived from multi-dimensional pivots.
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    Reason for 2 of 2
    ?
    • 1.The step from P2 to P3 commits the probabilistic fallacy of transposing the conditional: P(statistic|θ) cannot be inverted to P(θ|statistic) without Bayes' theorem.
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    • 2.Fisher's own repeated revisions and inability to generalize fiducial inference beyond one-parameter cases reveal the argument lacks a sound logical foundation.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The pivotal quantity \(\hat{\theta}(s) - \theta\) has a known distribution (normal with the aforementioned variance).
      ?

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    • 2.The distribution of the pivotal quantity is independent of the sample.
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    • 3.Fixing the sample to \(s\) fixes the value of \(\hat{\theta}\), which uniquely determines a distribution over the parameter values \(\theta\).
      ?

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    Strongest counterpoint
    Explore the most compelling reason on the other side.