Event Details

Statistics seminar in the School of Mathematical Sciences.

Title: Max-and-Smooth: Approximate Bayesian Inference in Latent Gaussian Models with a multivariate link function

Abstract: With modern high-dimensional data, complex statistical models are necessary, requiring computationally feasible inference schemes. We introduce Max-and-Smooth, an approximate Bayesian inference scheme for a flexible class of latent Gaussian models (LGMs). These models are such that one or more likelihood parameters are modeled by latent additive Gaussian processes, which calls for a multivariate link function. Our proposed inference scheme is a two-step approach. In the first step (Max), the likelihood function is approximated by a Gaussian density with mean and covariance equal to the maximum likelihood estimate and the inverse observed information, respectively. In the second step (Smooth), the latent parameters and hyperparameters are inferred and smoothed with the approximated likelihood function. The proposed method ensures that the uncertainty from the first step is correctly propagated to the second step. The prior densities for the latent parameters and the approximated likelihood function are Gaussian. Thus, the approximate conditional posterior density of the latent parameters is also Gaussian, which facilitates efficient posterior inference in high dimensions, especially when the Gaussian prior density is specified with a sparse precision matrix. The approximate marginal posterior distribution of the hyperparameters is tractable; thus, the hyperparameters can be sampled independently of the latent parameters. The proposed inference scheme is demonstrated on three spatially referenced real datasets, namely, (i) average surface air temperature in Europe over the summer period, (ii) flood frequency data from the UK, and (iii) extreme precipitation from the UK Climate Projections.