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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The conditions required for maximum likelihood estimation to be provably consistent do not apply to estimating tree topology

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Wald's (1949) consistency conditions apply to continuous parameters
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    • 2.Tree topologies are discrete, not continuous, parameters
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Steel and Matsen (2007) demonstrated that maximum likelihood can favor the wrong tree topology with probability approaching 1 under certain substitution models.
      ?

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    • 2.A consistent estimator cannot systematically converge on incorrect values as data increases, so topology estimation fails the formal definition of consistency in the frequentist sense.
      ?

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    • 3.The discreteness objection conflates the domain of parameters with the convergence properties that define consistency, leaving the core inapplicability claim intact.
      ?

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    Reason against 2 of 2
    ?
    • 1.Wald's consistency proof requires the parameter space to be compact, but the space of tree topologies grows super-exponentially with taxa count.
      ?

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    • 2.Non-compact discrete spaces violate identifiability conditions that Wald's framework presupposes, making consistency proofs inapplicable regardless of continuity distinctions.
      ?

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