Matteo Fasiolo (University of Bristol) – Multivariate Gaussian additive models with covariate-dependent covariance matrices

Dynamic covariance matrix models for multivariate normal data are a widely-applicable class of statistical models, meant to capture the covariate-dependent nature of the variance and dependence parameters. However, such models are rarely used in practice, partly due to the computational difficulties involved in model fitting. In particular, it is challenging to ensure the positive definiteness of the covariance matrix while guaranteeing computational scalability for even moderate dimension of the response vector. In this talk we will present methods for fitting multivariate Gaussian regression models where each parameter of the mean vector and of (an unconstrained parametrisation of) the covariance matrix can be modelled additively, via parametric or spline-based smooth effects. We will focus particularly on the modified Cholesky decomposition and we will show how the sparsity of the corresponding derivative system aids scalability w.r.t. the dimension of the response vector. The usefulness of the new models will be illustrated on a UK regional electrical net-demand forecasting application.