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Robustifying Likelihoods by Optimistically Re-weighting Data.

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|September 26, 2025
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Summary
This summary is machine-generated.

This study introduces Optimistically Weighted Likelihood (OWL) to address the brittleness of likelihood-based inferences caused by model misspecification. OWL robustifies statistical models by accounting for minor deviations from assumptions, improving reliability in real-world data analysis.

Keywords:
Coarsened BayesData contaminationMixture modelsModel misspecificationOutliersRobust inferenceTotal variation distance

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Likelihood-based inferences are widely used but sensitive to model misspecification.
  • Model misspecification, including outliers or incorrect assumptions, can significantly impact inference results, a problem termed 'brittleness'.

Purpose of the Study:

  • To address the brittleness problem in likelihood-based inferences.
  • To develop a robust statistical method that formally accounts for small amounts of model misspecification.

Main Methods:

  • Introduced Optimistically Weighted Likelihood (OWL) by selecting a model-friendly data-generating process within a neighborhood of the empirical measure.
  • Focused on total variation (TV) neighborhoods for theoretical analysis.
  • Developed estimation algorithms for practical application.

Main Results:

  • OWL robustifies the original likelihood by incorporating a mechanism to handle minor model misspecification.
  • Theoretical properties of OWL were studied.
  • Methodology was demonstrated through applications in mixture models and regression.

Conclusions:

  • Optimistically Weighted Likelihood (OWL) offers a robust alternative to traditional likelihood methods.
  • OWL effectively mitigates the impact of model misspecification, enhancing the reliability of statistical inferences.
  • The proposed methodology shows promise for applications in complex statistical modeling scenarios.