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Integrated nested Laplace approximations (INLA) is a method for approximate Bayesian inference based on Laplace's method.[1] It is designed for a class of models called latent Gaussian models (LGMs), for which it can be a fast and accurate alternative for Markov chain Monte Carlo methods to compute posterior marginal distributions.[2][3][4] Due to its relative speed even with large data sets for certain problems and models, INLA has been a popular inference method in applied statistics, in particular spatial statistics, ecology, and epidemiology.[5][6][7] It is also possible to combine INLA with a finite element method solution of a stochastic partial differential equation to study e.g. spatial point processes and species distribution models.[8][9] The INLA method is implemented in the R-INLA R package.[10]
- ^ Rue, Håvard; Martino, Sara; Chopin, Nicolas (2009). "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations". J. R. Statist. Soc. B. 71 (2): 319–392. doi:10.1111/j.1467-9868.2008.00700.x. hdl:2066/75507. S2CID 1657669.
- ^ Taylor, Benjamin M.; Diggle, Peter J. (2014). "INLA or MCMC? A tutorial and comparative evaluation for spatial prediction in log-Gaussian Cox processes". Journal of Statistical Computation and Simulation. 84 (10): 2266–2284. arXiv:1202.1738. doi:10.1080/00949655.2013.788653. S2CID 88511801.
- ^ Teng, M.; Nathoo, F.; Johnson, T. D. (2017). "Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods". Journal of Statistical Computation and Simulation. 87 (11): 2227–2252. doi:10.1080/00949655.2017.1326117. PMC 5708893. PMID 29200537.
- ^ Wang, Xiaofeng; Yue, Yu Ryan; Faraway, Julian J. (2018). Bayesian Regression Modeling with INLA. Chapman and Hall/CRC. ISBN 9781498727259.
- ^ Blangiardo, Marta; Cameletti, Michela (2015). Spatial and Spatio-temporal Bayesian Models with R-INLA. John Wiley & Sons, Ltd. ISBN 9781118326558.
- ^ Opitz, T. (2017). "Latent Gaussian modeling and INLA: A review with focus on space-time applications". Journal de la Société Française de Statistique. 158: 62–85. arXiv:1708.02723.
- ^ Moraga, Paula (2019). Geospatial Health Data: Modeling and Visualization with R-INLA and Shiny. Chapman and Hall/CRC. ISBN 9780367357955.
- ^ Lindgren, Finn; Rue, Håvard; Lindström, Johan (2011). "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach". J. R. Statist. Soc. B. 73 (4): 423–498. doi:10.1111/j.1467-9868.2011.00777.x. hdl:20.500.11820/1084d335-e5b4-4867-9245-ec9c4f6f4645. S2CID 120949984.
- ^ Lezama-Ochoa, N.; Grazia Pennino, M.; Hall, M. A.; Lopez, J.; Murua, H. (2020). "Using a Bayesian modelling approach (INLA-SPDE) to predict the occurrence of the Spinetail Devil Ray (Mobular mobular)". Scientific Reports. 10 (1): 18822. Bibcode:2020NatSR..1018822L. doi:10.1038/s41598-020-73879-3. PMC 7606447. PMID 33139744.
- ^ "R-INLA Project". Retrieved 21 April 2022.