Integrated nested Laplace approximations

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Bayesian statistics
Posterior = Likelihood × Prior ÷ Evidence
Background
Bayesian inference Bayesian probability Bayes' theorem Bernstein–von Mises theorem Coherence Cox's theorem Cromwell's rule Principle of indifference Principle of maximum entropy
Model building
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Posterior approximation
Markov chain Monte Carlo Laplace's approximation Integrated nested Laplace approximations Variational inference Approximate Bayesian computation
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Evidence approximation
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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]