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Related Experiment Video

Updated: Aug 5, 2025

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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Mathematical theory of Bayesian statistics for unknown information source.

Sumio Watanabe1

  • 1Department of Mathematical and Computing Science, Tokyo Institute of Technology, 2-12-1 Oookayama, Meguro-ku, Tokyo 52-8552, Japan.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 27, 2023
PubMed
Summary
This summary is machine-generated.

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This study introduces a mathematical theory for Bayesian statistics to address unknown uncertainty in models. It clarifies properties of cross-validation and information criteria, offering better estimators for generalization loss and marginal likelihood.

Area of Science:

  • Statistical Inference
  • Bayesian Statistics

Background:

  • Statistical models and prior distributions are acknowledged as fictional candidates.
  • Mathematical properties of cross-validation, information criteria, and marginal likelihood are not fully understood, especially with under- or over-parameterized models.

Purpose of the Study:

  • To introduce a mathematical theory for Bayesian statistics addressing unknown uncertainty.
  • To clarify general properties of statistical measures like cross-validation, information criteria, and marginal likelihood.
  • To provide a theoretical standpoint for users skeptical of specific models or priors.

Main Methods:

  • Development of a new mathematical theory for Bayesian statistics.
  • Analysis of cross-validation, information criteria, and marginal likelihood properties.
Keywords:
cross validationinformation criterionmarginal likelihood

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  • Application of new experiments to well-known results.

    • Main Results:

    • A more precise estimator for generalization loss than leave-one-out cross-validation was found.
    • A more accurate approximation of marginal likelihood than the Bayesian Information Criterion exists.
    • Optimal hyperparameters for generalization loss and marginal likelihood were shown to differ.

    Conclusions:

    • The new theory clarifies the properties of statistical measures under model uncertainty.
    • The findings offer improved methods for estimating generalization loss and marginal likelihood.
    • The research provides a robust framework for Bayesian inference when model assumptions are uncertain.