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.
Transport map accelerated Markov chain Monte Carlo.SIAM/ASA Journal on Uncertainty Quantification, 6(2):645–682, 2018
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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.