An importance sampling correction is added to integrated Laplace approximation so that the approximate posterior for latent Gaussian models converges to the true posterior as the number of samples grows.
Black box variational inference with a deterministic objective: Faster, more accurate, and even more black box.Journal of Machine Learning Research, 25(18):1–39
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Corrected Integrated Laplace Approximation for Bayesian Inference in Latent Gaussian Models
An importance sampling correction is added to integrated Laplace approximation so that the approximate posterior for latent Gaussian models converges to the true posterior as the number of samples grows.