LGM Split Sampler: An Efficient MCMC Sampling Scheme for Latent Gaussian Models

Abstract

A general and flexible class of latent Gaussian models is proposed in this paper. The latent Gaussian model is adapted to the generalized additive model for location, scale and shape (GAMLSS), that is, the data density function of each data point can depend on more than a single linear predictor of the latent parameters. We refer to this framework as extended latent Gaussian models. The most commonly applied latent Gaussian models (LGMs) are such that a linear predictor is proposed only for the location parameter. Extended LGMs allow proposing linear predictors also for the scale parameter and potentially other parameters. We propose a novel computationally efficient Markov chain Monte Carlo sampling scheme for the extended LGMs which we refer to as the LGM split sampler. It is a two block Gibbs sampling scheme designed to exploit the model structure of the extended LGMs. An extended LGM is constructed for a simulated dataset and the LGM split sampler is implemented for posterior simulations. The results demonstrate the flexibility of the extended LGM framework and the efficiency of the LGM split sampler.