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    Fixing the observed sample s does not transform a samplin... — Carmelics
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    Challenges→The fiducial argument allows construction of a probability distribution over parameter values based on the observed sample.

    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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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Sampling distributions describe the behavior of statistics across hypothetical repeated samples, not the uncertainty of unknown fixed parameters.
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    • 2.Without a prior, there is no mathematical mapping from likelihood function to posterior probability over parameters, only relative plausibility.
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    • 3.Frequentist probability quantifies long-run frequencies; parameters don't have frequencies, so fixed parameters cannot have probability distributions.
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    Reasons Against

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    • 1.Confidence intervals and hypothesis tests use sampling distributions to make valid inferences about fixed parameters without explicit priors.
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    • 2.Conditioning on observed data is mathematically valid via likelihood principle; invoking a prior is an additional assumption, not a requirement.
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    • 3.The distinction between epistemic and ontic probability allows fixed parameters to have well-defined probability distributions representing rational uncertainty.
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    Related

    Conditioning on observed data is mathematically valid via likelihood principle; ...Confidence intervals and hypothesis tests use sampling distributions to make val...Frequentist probability quantifies long-run frequencies; parameters don't have f...Sampling distributions describe the behavior of statistics across hypothetical r...
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    The distinction between epistemic and ontic probability allows fixed parameters ...The fiducial argument allows construction of a probability distribution over par...Without a prior, there is no mathematical mapping from likelihood function to po...

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