Thursday 10 May 2018: Statistical Science seminar- Birgir Hrafnkelsson "Fast computation for latent Gaussian models with a multivariate link function"
Birgir Hrafnkelsson -
Latent Gaussian models (LGMs) form a frequently used class within Bayesian hierarchical models. This class is such that the density of the observed data conditioned 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 location parameter, the scale parameter and the shape parameter of an observation are transformed into three latent parameters. These three 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. Another benefit of this approach is fast subset selection at the latent level. The computational approach is applied to; (i) annual maximum peak flow series from UK and (ii) data for fitting regression lines on multiple grid points.