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    Selecting which hypotheses to include in a likelihood rat... — Carmelics
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    Challenges→Likelihoodists, who reject Bayesian prior probabilities, may still embrace the Likelihood Ratio Convergence Theorem.

    Selecting which hypotheses to include in a likelihood ratio comparison is not itself licensed by likelihoods alone, requiring a prior probability-like commitment.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Likelihood ratios only compare hypotheses already in the set; they cannot justify why those specific hypotheses deserve comparison over alternatives.
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    • 2.The problem of auxiliary hypotheses shows that model selection requires background assumptions about which confounders and variables matter—inherently prior-like.
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    • 3.Without prior constraints on hypothesis space, likelihood ratios would equally support infinitely many unfalsifiable hypotheses, making inference incoherent.
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    Reasons Against

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    • 1.Hypothesis selection can be grounded in domain-specific empirical constraints and parsimony principles, not requiring subjective prior commitments.
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    • 2.The demarcation between 'selecting hypotheses' and 'assigning likelihoods' is arbitrary; both are continuous acts of model specification, not fundamentally different.
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    • 3.If likelihoods alone require priors for hypothesis selection, priors themselves face the same regress problem—no position avoids circular justification.
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    Related

    Hypothesis selection can be grounded in domain-specific empirical constraints an...If likelihoods alone require priors for hypothesis selection, priors themselves ...Likelihood ratios only compare hypotheses already in the set; they cannot justif...Likelihoodists, who reject Bayesian prior probabilities, may still embrace the L...
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    The demarcation between 'selecting hypotheses' and 'assigning likelihoods' is ar...The problem of auxiliary hypotheses shows that model selection requires backgrou...Without prior constraints on hypothesis space, likelihood ratios would equally s...

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