Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations
Abstract
Summary Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes…
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Applying a bootstrap technique with the percentile method to each time series yields a 95% confidence interval for the original lowess fit.
“In addition, we applied a bootstrap technique to each time series with the percentile method, in order to account for the variability in the original lowess fit. With this methodology, each series would have a 95% confidence interval for the original lowess [28, 29].”
From Shift in Tuna Catches Due to Ocean Warming (2017) · cites this paper as [29]
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“Integrated Nested Laplace Approximation (INLA) was used to estimate the Bayesian hierarchical model [17, 27, 28].”
Method
- Authors
- Rue, H., Martino, S., & Chopin, N.
- Affiliations
- Norwegian University of Science and Technology (NO)
- Centre de Recherche en Économie et Statistique (FR)
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2009-04-01
- Volume
- 71
- Issue
- 2
- Pages
- 319-392
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2144898279
- Cited by
- 5,279
- References
- 3
- Citations by year
- 2026: 418 · 2025: 497 · 2024: 430 · 2023: 419 · 2022: 494 · 2021: 485 · 2020: 424 · 2019: 384 · 2018: 307 · 2017: 252 · 2016: 241 · 2015: 238 · 2014: 179 · 2013: 164 · 2012: 142
- FWCI
- 90.75
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- HAL (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Radboud Repository (Radboud University) (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion)
- Funders
- Economic and Social Research Council (ES/F032242/1)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- latent Gaussian models, integrated nested Laplace approximation, approximate Bayesian inference, computational efficiency, model comparison, Markov chain Monte Carlo alternatives
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