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Inflated Density Ratio and Its Variation and Generalization for Computing Marginal Likelihoods.
Yu-Bo Wang1, Ming-Hui Chen2, Wei Shi2
1School of Mathematical and Statistical Sciences, Clemson University.
Journal of the Korean Statistical Society
|October 19, 2020
Summary
This study introduces new methods, dimension reduced inflated density ratio (Dr.IDR) and general dimension reduced (GDr) estimators, to compute marginal likelihood in Bayesian analysis. These methods improve upon existing techniques for model comparison and variable selection.
Area of Science:
- Bayesian statistics
- Computational statistics
Background:
- Marginal likelihood is crucial for Bayesian variable selection and model comparison.
- Calculating marginal likelihood is often analytically intractable due to model complexity.
Purpose of the Study:
- To examine the properties of the inflated density ratio (IDR) method for computing marginal likelihood.
- To develop and evaluate novel estimators, Dr.IDR and GDr, for marginal likelihood computation.
Main Methods:
- Monte Carlo (MC) and Markov chain Monte Carlo (MCMC) sampling.
- Development of dimension reduced inflated density ratio (Dr.IDR) and general dimension reduced (GDr) estimators.
- Simulation studies to assess empirical performance of IDR, Dr.IDR, and GDr estimators.
Main Results:
- The study examines the properties of the IDR method.
- New Dr.IDR and GDr estimators are developed.
- Simulation studies demonstrate the performance of the proposed estimators.
Conclusions:
- The developed Dr.IDR and GDr estimators offer improved methods for marginal likelihood computation.
- The GDr estimator is useful for calculating normalizing constants, as shown in a case study on inequality-constrained analysis of variance.
- These advancements aid in Bayesian model comparison and variable selection.
Keywords:
62-M0562F15CMDEConditional posterior densityConstrained parameter spaceIWMDEMarginal posterior densityMore Related Videos
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