On the use of marginal posteriors in marginal likelihood estimation via importance sampling

2013/11/30 by K. Perrakis, Konstantinos Perrakis, Ioannis Ntzoufras +3 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computer science #Estimation theory #Estimator #Importance sampling #Likelihood function #Marginal likelihood #Marginal model #Markov chain Monte Carlo #Mathematics #Maximum likelihood #Monte Carlo method #Regression analysis #Sampling (signal processing) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics #stat.CO

paper · pdf · doi:10.1016/j.csda.2014.03.004

published as Computational Statistics & Data Analysis Volume 77, September 2014, Pages 54-69

arxiv created 2014/01/11 · openalex publication_date 2014/03/22 · arxiv updated 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate the efficiency of a marginal likelihood estimator where the product of the marginal posterior distributions is used as an importance-sampling function. The approach is generally applicable to multi-block parameter vector settings, does not require additional Markov Chain Monte Carlo (MCMC) sampling and is not dependent on the type of MCMC scheme used to sample from the posterior. The proposed approach is applied to normal regression models, finite normal mixtures and longitudinal Poisson models, and leads to accurate marginal likelihood estimates.

Citations

• Annealed importance sampling
• Expectation Propagation for approximate Bayesian inference
• Sequential Monte Carlo Samplers
• Inference from Iterative Simulation Using Multiple Sequences
• Annealed Importance Sampling
• Approximating the marginal likelihood in mixture models
• Bayes Factors
• Sampling-Based Approaches to Calculating Marginal Densities

Cited by

• Easily Computed Marginal Likelihoods for Multivariate Mixture Models Using the THAMES Estimator
• Revisiting Proxima with ESPRESSO

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• Robustly estimating the marginal likelihood for cognitive models via importance sampling