Approximating evidence via bounded harmonic means

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.