Estimating the marginal likelihood with Integrated nested Laplace approximation (INLA)
Abstract
The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities of interest. For many complex models, including latent modeling approaches, marginal likelihoods are however difficult to compute. One recent promising approach for approximating the marginal likelihood is Integrated Nested Laplace Approximation (INLA), design for models with latent Gaussian structures. In this study we compare the approximations obtained with INLA to some alternative approaches on a number of examples of different complexity. In particular we address a simple linear latent model, a Bayesian linear regression model, logistic Bayesian regression models with probit and logit links, and a Poisson longitudinal generalized linear mixed model.
Related
- Efficient model exploration with the integrated nested Laplace approximation
- Simulation-consistent Estimation of the Marginal Likelihood for Block Models
- High-Dimensional Two-Sample Inference via Marginal Likelihood-Ratio Rank Statistics
- Marginal maximum likelihood estimation and asymptotic theory for latent variable models in high dimensions
- Marginal Composite Likelihood Estimation of Bergomi Models from High-Frequency Option Prices
BibTeX
@article{hubin2026estimating,
title = {{Estimating the marginal likelihood with Integrated nested Laplace approximation (INLA)}},
author = {Aliaksandr Hubin and Geir Olve Storvik},
year = {2026},
month = oct,
doi = {10.68365/jrepstat.2026.9},
url = {https://doi.org/10.68365/jrepstat.2026.9},
note = {CC BY},
}
RIS
TY - JOUR
TI - Estimating the marginal likelihood with Integrated nested Laplace approximation (INLA)
AU - Aliaksandr Hubin
AU - Geir Olve Storvik
PY - 2026
DA - 2026/10/26
DO - 10.68365/jrepstat.2026.9
UR - https://doi.org/10.68365/jrepstat.2026.9
AB - The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities of interest. For many complex models, including latent modeling approaches, marginal likelihoods are however difficult to compute. One recent promising approach for approximating the marginal likelihood is Integrated Nested Laplace Approximation (INLA), design for models with latent Gaussian structures. In this study we compare the approximations obtained with INLA to some alternative approaches on a number of examples of different complexity. In particular we address a simple linear latent model, a Bayesian linear regression model, logistic Bayesian regression models with probit and logit links, and a Poisson longitudinal generalized linear mixed model.
ER -