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    A consistent estimator cannot systematically converge on ... — Carmelics
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    Supports→The conditions required for maximum likelihood estimation to be provably consistent do not apply to estimating tree topology

    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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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Topology estimation often selects among discrete, inequivalent structures, making convergence to a wrong structure a genuine failure mode.
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    • 2.Standard consistency requires probability of error → 0 as n → ∞; topology methods often have bounded error rates for finite n.
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    • 3.Misspecification in phylogenetic/graphical models can cause systematic bias that doesn't vanish with more data under standard assumptions.
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    Reasons Against

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    Reason against
    ?
    • 1.Consistency formally requires convergence to true parameter under correct model; topology methods may be consistent under their own assumptions.
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    • 2.Many topology estimators (e.g., maximum likelihood, Bayesian methods) are provably consistent given sufficient data and identifiability conditions.
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    • 3.Failure to converge to 'incorrect values' depends on how consistency is defined—weak vs. strong convergence, or convergence in probability vs. almost surely.
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    Key Terms

    Consistency (in frequentist sense)(statistics and epistemology)
    In frequentist statistics, a method is consistent if it reliably produces correct answers when you have lots of data.
    Consistent estimator(statistics and philosophy of science)
    A method for calculating an answer from data that gets more accurate the more data you collect, eventually zeroing in on the true answer.
    Converge(describing how existence and essence might relate for necessary beings)
    Come together or merge into the same thing; stop being separate.
    Formal definition(philosophy and mathematics)
    An official, precise description of what something means, using strict logical rules.
    Frequentist(contrasted with subjective Bayesian approach)
    An approach to probability that defines it as the long-run frequency of something happening—essentially, if you repeat an experiment many times, how often does the outcome occur?
    Systematically(as describing a consistent problem with voting methods)
    Happening as a regular pattern or built-in feature of how something works, rather than by accident or rarely.
    Topology estimation(statistics and data analysis)
    A method for figuring out the shape or structure of something (like networks or data patterns) based on observations.

    Connections

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    Truth & Knowledge1 linkedSkepticism1 linked

    Related

    Consistency formally requires convergence to true parameter under correct model;...Failure to converge to 'incorrect values' depends on how consistency is defined—...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Many topology estimators (e.g., maximum likelihood, Bayesian methods) are provab...
    Misspecification in phylogenetic/graphical models can cause systematic bias that...
    +3 moreShow less
    Standard consistency requires probability of error → 0 as n → ∞; topology method...The conditions required for maximum likelihood estimation to be provably consist...Topology estimation often selects among discrete, inequivalent structures, makin...