Extending integrated nested Laplace approximation to a class of near-Gaussian latent models. This work extends the integrated nested Laplace approximation (INLA) method to latent models outside the scope of latent Gaussian models, where independent components of the latent field can have a near-Gaussian distribution. The proposed methodology is an essential component of a bigger project that aims to extend the R package INLA in order to allow the user to add flexibility and challenge the Gaussian assumptions of some of the model components in a straightforward and intuitive way. Our approach is applied to two examples, and the results are compared with that obtained by Markov chain Monte Carlo, showing similar accuracy with only a small fraction of computational time. Implementation of the proposed extension is available in the R-INLA package.

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  1. Edgar Santos-Fernandez, Jay M. Ver Hoef, James M. McGree, Daniel J. Isaak, Kerrie Mengersen, Erin E. Peterson: SSNbayes: An R package for Bayesian spatio-temporal modelling on stream networks (2022) arXiv
  2. Castro-Camilo, Daniela; Mhalla, Linda; Opitz, Thomas: Bayesian space-time gap filling for inference on extreme hot-spots: an application to Red Sea surface temperatures (2021)
  3. Dawkins, Laura C.; Williamson, Daniel B.; Mengersen, Kerrie L.; Morawska, Lidia; Jayaratne, Rohan; Shaddick, Gavin: Where is the clean air? A Bayesian decision framework for personalised cyclist route selection using R-INLA (2021)
  4. Francisco Palmí-Perales, Virgilio Gómez-Rubio, Miguel A. Martinez-Beneito: Bayesian Multivariate Spatial Models for Lattice Data with INLA (2021) not zbMATH
  5. Gressani, Oswaldo; Lambert, Philippe: Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines (2021)
  6. Kuschnig, N., Vashold, L.: BVAR: Bayesian Vector Autoregressions with Hierarchical Prior Selection in R (2021) not zbMATH
  7. Osmundsen, Kjartan Kloster; Selland Kleppe, Tore; Liesenfeld, Roman: Importance sampling-based transport map Hamiltonian Monte Carlo for Bayesian hierarchical models (2021)
  8. Umlauf, N., Klein, N., Simon, T., Zeileis, A: bamlss: A Lego Toolbox for Flexible Bayesian Regression (and Beyond) (2021) not zbMATH
  9. van Niekerk, Janet; Bakka, Haakon; Rue, Håvard: Competing risks joint models using R-INLA (2021)
  10. van Niekerk, Janet; Rue, Håvard: Skewed probit regression -- identifiability, contraction and reformulation (2021)
  11. van Niekerk, J.; Bakka, H.; Rue, H.: A principled distance-based prior for the shape of the Weibull model (2021)
  12. Van Niekerk, J., Bakka, H., Rue, H., Schenk, O. : New Frontiers in Bayesian Modeling Using the INLA Package in R (2021) not zbMATH
  13. Wang, Craig; Furrer, Reinhard: Combining heterogeneous spatial datasets with process-based spatial fusion models: a unifying framework (2021)
  14. Watson, Joe; Joy, Ruth; Tollit, Dominic; Thornton, Sheila J.; Auger-Méthé, Marie: Estimating animal utilization distributions from multiple data types: a joint spatiotemporal point process framework (2021)
  15. Yaqiong Wang, Francesco Finazzi, Alessandro Fasso: D-STEM v2: A Software for Modeling Functional Spatio-Temporal Data (2021) not zbMATH
  16. Bolin, David; Kirchner, Kristin: The rational SPDE approach for Gaussian random fields with general smoothness (2020)
  17. Drori, Iddo: Deep variational inference (2020)
  18. Fuglstad, Geir-Arne; Hem, Ingeborg Gullikstad; Knight, Alexander; Rue, Håvard; Riebler, Andrea: Intuitive joint priors for variance parameters (2020)
  19. Gianluca Baio: survHE: Survival Analysis for Health Economic Evaluation and Cost-Effectiveness Modeling (2020) not zbMATH
  20. Lázaro, E.; Armero, C.; Gómez-Rubio, V.: Approximate Bayesian inference for mixture cure models (2020)

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