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A novel computationally efficient Markov chain Monte Carlo (MCMC) scheme forlatent Gaussian models (LGMs) is proposed in this paper. The sampling scheme isa two block Gibbs sampling scheme designed to exploit the model structure ofLGMs. We refer to the proposed sampling scheme as the MCMC split sampler. Theprinciple idea behind the MCMC split sampler is to split the latent Gaussianparameters into two vectors. The former vector consists of latent parameterswhich appear in the data density function, while the latter vector consists oflatent parameters which do not appear in it. The former vector is placed in thefirst block of the proposed sampling scheme and the latter vector is placed inthe second block along with any potential hyperparameters. The resultingconditional posterior density functions within the blocks allow the MCMC splitsampler to handle, by design, LGMs with latent models imposed on more than justthe mean structure of the data density function. The MCMC split sampler is alsodesigned to be applicable for any choice of a parametric data density function.Moreover, it scales well in terms of computational efficiency when thedimension of the latent model increase.

The MCMC split sampler: A block Gibbs sampling scheme for latent Gaussian models