Variant functional approximations for latent Gaussian models

The integrated nested Laplace approximation (INLA) [Rue et al., 2009] is now a well-known functional approximation algorithm for implementing Bayesian inference in latent Gaussian models but has some limitations: it is unable to handle a high dimensional model parameter θ, and makes a poor approximation when the posterior is multi-modal and the likelihood is highly nonGaussian. Two types of algorithm are proposed to address these limitations: (a) a combination of INLA and Monte Carlo methods and (b) analytic approximations with higher order moments. We test the performance of algorithms on a nonlinear stochastic velocity model for exchange current rate data between Euros and Dollars and a factor analysis model with both synthetic datasets and real data from multi-spectral extra-terrestrial microwave maps.