Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

By Håvard Rue, Sara Martino, Nicolas Chopin. 2009

5,252 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Effective Bayesian Modeling of Groups of Related Count Time Series (2014, methodology): “Should additional accuracy be required in the Laplace approximation, one could turn to a numerical integration technique for hyperparameters of models equipped with GMRF priors, the so-called integrated nested Laplace approximation (INLA, Rue et al., 2009).”
Stochastic Back-propagation and Variational Inference in Deep Latent Gaussian Models (2014, methodology): “For latent Gaussian models, other alternative inference algorithms have been proposed: the Integrated Nested Laplace Approximation (INLA) has been popular, but it is limited to models with very few hyperparameters (Rue et al., 2009).”
Bayesian Deep Learning and a Probabilistic Perspective of Generalization (2020, background): “Other standard deterministic approximations include Laplace [e.g., 27], EP [32], and INLA [43].”
Edward: A library for probabilistic modeling, inference, and criticism (2016, methodology): “This extends to many algorithms: for example, classical message passing, which performs exact local inferences; Gibbs sampling, which draws samples from conditionally conjugate inferences (Geman and Geman, 1984); expectation propagation, which locally minimizes KL(p||q) over exponential families (Mi”
Variational bounds for mixed-data factor analysis (2010, methodology): “It might be an interesting alternative to a Laplace approximation to the posterior, which is used in [KPBSK10, RMC09].”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “…ABC techniques, described in more details below, but also variational Bayes (Jaakkola and Jordan 2000), empirical likelihood (Owen 2001), integrated nested Laplace approximation (INLA) (Rue et al. 2009) and other solutions that relyonpseudo-models, or onsummarised versions of the data, or both.”
INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, methodology): “Routine calculations show that the GP density with the above link function is log-concave with respect to the predictor log { κ q ( s, t ) } , which is beneﬁcial for INLA and optimization routines in general.”
The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling (2017, background): “…linear Gaussian Markov random fields; Chan and Jeliazkov (2009) and McCausland, Miller, and Pelletier (2011) for linear Gaussian state–space models; Rue, Martino, and Chopin (2009) for nonlinear Markov random fields; McCausland (2012), Chan, Koop, and Potter (2013), Chan and Strachan (2014), and…”
Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation (2017, methodology): “An alternative approach is to use central composite design (Rue et al., 2009; Vanhatalo et al., 2010).”
Efficient Sampling for Gaussian Process Inference using Control Variables (2008, background): “Other applications of Gaussian processes where inference is intractable arise in spatio-temporal models and geostatistics and deterministic approximations have also been developed there [14].”
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, methodology): “Such problems arise frequently in applied statistics and examples include inference for the parameters of spatio-temporal models (Rue et al., 2009; Lyne et al., 2013), regression models with random effects (Fahrmeir and Lang, 2001), time-series models (West and Harrison, 1997), and selection between”
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, methodology): “For identifiability reasons, intrinsic models can be preferable, but alternatives such as conditioning on zero integral for the field can also be used, and are implemented in R-INLA.”
glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling (2017, methodology): “Several R packages are available for ﬁtting zero-inﬂated models: pscl , INLA , MCMCglmm , glmmADMB , mgcv , brms , and gamlss (Table 1; Zeileis et al., 2008; Rue et al., 2009; Hadﬁeld, 2010; Skaug et al., 2012; Wood et al., 2016; Bürkner, 2017; Stasinopoulos et al., 2017).”