Bayesian Computing with INLA: A Review
Abstract
The key operation in Bayesian inference, is to compute highdimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre Simon Laplace (1774). This simple idea approximates the integrand with a second order Taylor expansion around the mode and computes the integral analytically. By developing a nested version of this classical idea, combined with modern numerical techniques for sparse matrices, we obtain the approach of Integrated Nested Laplace Approximations (INLA) to do approximate Bayesian inference for latent Gaussian models (LGMs). LGMs represent an important modelabstraction for Bayesian inference and include a large proportion of the statistical models used today. In this review, we will discuss the reasons for the success of the INLAapproach, the RINLA package, why it is so accurate, why the approximations are very quick to compute and why LGMs make such a useful concept for Bayesian computing.
 Publication:

Annual Review of Statistics and Its Application
 Pub Date:
 March 2017
 DOI:
 10.1146/annurevstatistics060116054045
 arXiv:
 arXiv:1604.00860
 Bibcode:
 2017AnRSA...4..395R
 Keywords:

 Statistics  Methodology
 EPrint:
 28 pages, 7 figures