Importance Sampling with the Integrated Nested Laplace Approximation

The integrated nested Laplace approximation (INLA) is a deterministic approach to Bayesian inference on latent Gaussian models (LGMs) and focuses fast accurate of posterior marginals for the parameters in models. Recently, methods have been developed extend this class those that can be expressed as conditional LGMs by fixing some descriptive values. These differ manner values are chosen. This article proposes combine importance sampling with INLA (IS-INLA), extends more robust adaptive multiple algorithm combined (AMIS-INLA). gives comparison between these approaches existing series applications simulated observed datasets evaluates their performance based accuracy, efficiency, robustness. validated exact posteriors simple bivariate linear model; then, they applied lasso model, Poisson mixture, zero-inflated model spatial autoregressive model. show AMIS-INLA approach, general, outperforms other compared, but IS-INLA could considered faster when good proposals available. Supplementary materials available online.