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On partial likelihood and the construction of factorisable transformations.

H S Battey1, D R Cox2, Su Hyeong Lee3

  • 1Department of Mathematics, Imperial College London, London, UK.

Information Geometry
|November 24, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a systematic method for simplifying statistical models by eliminating nuisance parameters using partial likelihood. The approach aids both Bayesian and frequentist inferences, especially with many nuisance parameters.

Keywords:
Inferential separationMarginal likelihoodMatched comparisonsMethod of characteristicsNuisance parametersPartial differential equations

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Area of Science:

  • Statistics
  • Mathematical Statistics
  • Computational Statistics

Background:

  • Partial likelihood is crucial for eliminating nuisance parameters in statistical inference.
  • Marginal likelihood factorizations are challenging to compute directly.
  • Nuisance parameters complicate Bayesian and frequentist analyses, especially when numerous.

Purpose of the Study:

  • To develop a systematic approach for finding data transformations that yield marginal likelihoods free of nuisance parameters.
  • To generalize this method for situations where exact factorizable structure is not present.
  • To provide a novel construction applicable beyond statistical inference.

Main Methods:

  • Focus on marginal likelihood factorizations and their computational difficulties.
  • Propose a method based on solving an integro-differential equation derived from Laplace transforms.
  • Candidate solutions satisfy a simpler first-order linear homogeneous differential equation.

Main Results:

  • A systematic procedure for identifying data transformations that simplify likelihood functions.
  • The method is generalized to handle approximate factorizable structures.
  • Illustrative examples demonstrate the practical application of the approach.

Conclusions:

  • The proposed method offers a systematic way to handle nuisance parameters in statistical modeling.
  • This technique is valuable for both Bayesian and frequentist inference, enhancing computational efficiency.
  • The mathematical construction has potential applications in diverse scientific fields beyond statistics.