2021/03/03 by Martin Outzen Berild, Berild, Martin Outzen, Sara Martino +5 · 2 citations
Decision Sciences · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2103.02721
openalex publication_date 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Integrated Nested Laplace Approximation (INLA) is a deterministic approach to Bayesian inference on latent Gaussian models (LGMs) and focuses on fast and accurate approximation of posterior marginals for the parameters in the models. Recently, methods have been developed to extend this class of models to those that can be expressed as conditional LGMs by fixing some of the parameters in the models to descriptive values. These methods differ in the manner descriptive values are chosen. This paper proposes to combine importance sampling with INLA (IS-INLA), and extends this approach with the more robust adaptive multiple importance sampling algorithm combined with INLA (AMIS-INLA). This paper gives a comparison between these approaches and existing methods on a series of applications with simulated and observed datasets and evaluates their performance based on accuracy, efficiency, and robustness. The approaches are validated by exact posteriors in a simple bivariate linear model; then, they are applied to a Bayesian lasso model, a Bayesian imputation of missing covariate values, and lastly, in parametric Bayesian quantile regression. The applications show that the AMIS-INLA approach, in general, outperforms the other methods, but the IS-INLA algorithm could be considered for faster inference when good proposals are available.