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Approximating evidence via bounded harmonic means.

Dana Naderi1, Christian P Robert1,2, Kaniav Kamary3

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Summary
This summary is machine-generated.

A new Elliptical Covering Marginal Likelihood Estimator (ECMLE) improves Bayesian model selection by addressing the infinite-variance issue of the harmonic mean estimator (HME). ECMLE offers more stable evidence approximations, even in complex scenarios.

Keywords:
HPD regionHarmonic mean estimatorMarginal likelihoodModel evidenceNormalizing constantRosenbrock distribution

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Area of Science:

  • Bayesian statistics
  • Computational statistics
  • Model selection

Background:

  • Bayesian model selection requires computing model evidence (marginal likelihood), often an intractable integral.
  • The harmonic mean estimator (HME) is a standard but potentially high-variance method for approximating model evidence.
  • Previous work standardized HME using instrumental functions, including higher posterior density (HPD) indicators.

Purpose of the Study:

  • To develop a novel, practical estimator for marginal likelihood computation.
  • To overcome the infinite-variance issue inherent in the original harmonic mean estimator.
  • To provide a robust method for model evidence approximation in both unimodal and multimodal settings.

Main Methods:

  • Proposed the Elliptical Covering Marginal Likelihood Estimator (ECMLE).
  • Utilizes an elliptical covering of the higher posterior density (HPD) region with non-overlapping ellipsoids.
  • Enables exact volume computations and application in multimodal distributions.

Main Results:

  • ECMLE eliminates the infinite-variance problem of the standard HME.
  • Demonstrates superior performance compared to existing methods like THAMES.
  • Exhibits lower variance and more stable evidence approximations, particularly in challenging settings.

Conclusions:

  • ECMLE offers a robust and efficient solution for marginal likelihood computation in Bayesian inference.
  • The method is suitable for complex, multimodal distributions.
  • ECMLE represents a significant advancement in approximating model evidence for improved Bayesian model selection.