On the Fully Bayesian Treatment of Latent Gaussian Models using Stochastic Simulations

Latent Gaussian models (LGMs) are extensively used in data analysis given their flexible modeling capabilities and interpretability. The fully Bayesian treatment of LGMs is usually intractable, and therefore it is necessary to resort to approximations. This paper proposes the use of stochastic simulations based on Markov chain Monte Carlo (MCMC) methods for small to moderately sized data sets and for LGMs comprising a set of parameters that prevents the use of quadrature techniques. We discuss the challenges in applying MCMC methods to LGMs and compare different strategies based on efficient parametrizations and efficient proposal mechanisms. Extensive evaluation on simulated and real data suggests a sampling strategy that achieves high efficiency with moderate cost compared to state-of-the-art methods for the fully Bayesian treatment of LGMs