Approximate posterior inference for latent Gaussian models with a multivariate link function
Birgir Hrafnkelsson, Department of Mathematics, School of Engineering and Natural Resources - University of Iceland
Latent Gaussian models (LGMs) form a frequently used class within Bayesian hierarchical models. This class is such that the density of the observed data conditional on the latent parameters can be any parametric density, and the prior density of the latent parameters is Gaussian. Typically, the link function is univariate, i.e., it is only a function of the location parameter. Here the focus is on LGMs with a multivariate link function, e.g., LGMs structured such that the K parameters in the data density of each observation are transformed to K latent parameters. These K latent parameters are modeled with a linear model at the latent level. The parameters within the linear model are also defined as latent parameters and thus assigned a Gaussian prior density. To facilitate fast posterior computation, a Gaussian approximation is proposed for the likelihood function of the parameters. This approximation, along with a priori assumption of Gaussian latent parameters, allows for straightforward sampling from the posterior density. The computational approach is demonstrated on; (i) linear regression models on multiple grid points for the prediction of surface air temperature with global climate model ensemble; (ii) annual maximum peak flow series from UK.
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