Easily Computed Marginal Likelihoods from Posterior Simulation Using the THAMES Estimator.

Area of Science:

• Statistics
• Computational Statistics
• Bayesian Inference

Background:

• Estimating marginal likelihoods is crucial for model selection in Bayesian analysis.
• Existing methods can be computationally intensive or require additional simulations.
• There is a need for efficient and accessible estimators.

Purpose of the Study:

• To propose a novel, easily computed estimator for marginal likelihoods.
• To combine and improve upon existing reciprocal importance sampling techniques.
• To provide a computationally efficient tool for Bayesian model comparison.

Main Methods:

• Utilizing reciprocal importance sampling with unnormalized posterior densities.
• Building upon the work of DiCiccio et al. (1997) and Robert and Wraith (2009).
• Incorporating a simple Monte Carlo approximation for constrained parameter spaces.

Main Results:

• The proposed estimator is unbiased for the reciprocal of the marginal likelihood.
• The estimator demonstrates consistency, finite variance, and asymptotic normality.
• An optimal method for specifying the user-defined control parameter is derived.

Conclusions:

• The new estimator offers a computationally efficient and statistically sound approach to marginal likelihood estimation.
• It simplifies Bayesian inference by leveraging existing posterior simulation output.
• The method is robust and adaptable to both constrained and unconstrained parameter spaces.