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    The Likelihood Ratio Convergence Theorem's practical appl... — Carmelics
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    Challenges→Likelihoodists, who reject Bayesian prior probabilities, may still embrace the Likelihood Ratio Convergence Theorem.

    The Likelihood Ratio Convergence Theorem's practical application requires specifying a hypothesis space, and delimiting that space embeds prior probabilistic judgments.

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    Reasons For

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    • 1.Any finite hypothesis space requires prior selection; excluding possibilities is itself a probabilistic commitment.
      ?

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    • 2.The theorem assumes a fixed space, but real inquiry requires choosing which hypotheses to consider initially.
      ?

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    • 3.Likelihood ratios converge only within the chosen space; alternative spaces yield different convergence patterns.
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    Reasons Against

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    Reason against
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    • 1.Specifying a space need not embed priors; it can simply reflect background knowledge independent of probability.
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    • 2.The theorem's validity holds regardless of how the space was chosen; the claim conflates justification with application.
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    • 3.Empirical data itself can overcome initial space choices through model comparison and expansion.
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    Related

    Any finite hypothesis space requires prior selection; excluding possibilities is...Empirical data itself can overcome initial space choices through model compariso...Likelihood ratios converge only within the chosen space; alternative spaces yiel...Likelihoodists, who reject Bayesian prior probabilities, may still embrace the L...
    +3 moreShow less
    Specifying a space need not embed priors; it can simply reflect background knowl...The theorem assumes a fixed space, but real inquiry requires choosing which hypo...The theorem's validity holds regardless of how the space was chosen; the claim c...

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